Below you find an interactive list of all my publications, which can be filtered by keywords, year, publication type and coauthors. There are also static lists of my books/book-chapters as well as journal and conference publications.

## 2019 |

Lee, Jin Gyu; Berger, Thomas; Trenn, Stephan; Shim, Hyungbo Utility of edge-wise funnel coupling for asymptotically solving distributed consensus optimization Unpublished 2019, (submitted for publication). Abstract | Links | BibTeX | Tags: CDC, funnel-control, networks, nonlinear, synchronization, vidi @unpublished{LeeBerg19pp, title = {Utility of edge-wise funnel coupling for asymptotically solving distributed consensus optimization}, author = {Jin Gyu Lee and Thomas Berger and Stephan Trenn and Hyungbo Shim}, url = {https://stephantrenn.net/wp-content/uploads/2019/10/Preprint-LBTS191001.pdf, Preprint}, year = {2019}, date = {2019-10-01}, abstract = {A new approach to distributed consensus optimization is studied in this paper. The cost function to be minimized is a sum of local cost functions which are not necessarily convex as long as their sum is convex. This benefit is obtained from a recent observation that, with a large gain in the diffusive coupling, heterogeneous multi-agent systems behave like a single dynamical system whose vector field is simply the average of all agents' vector fields. However, design of the large coupling gain requires global information such as network structure and individual agent dynamics. In this paper, we employ a nonlinear time-varying coupling of diffusive type, which we call `edge-wise funnel coupling.' This idea is borrowed from adaptive control, which enables decentralized design of distributed optimizers without knowledge of global information. Remarkably, without a common internal model, each agent achieves asymptotic consensus to the optimal solution of the global cost. We illustrate this result by a network that asymptotically finds the least-squares solution of a linear equation in a distributed manner.}, note = {submitted for publication}, keywords = {CDC, funnel-control, networks, nonlinear, synchronization, vidi}, pubstate = {published}, tppubtype = {unpublished} } A new approach to distributed consensus optimization is studied in this paper. The cost function to be minimized is a sum of local cost functions which are not necessarily convex as long as their sum is convex. This benefit is obtained from a recent observation that, with a large gain in the diffusive coupling, heterogeneous multi-agent systems behave like a single dynamical system whose vector field is simply the average of all agents' vector fields. However, design of the large coupling gain requires global information such as network structure and individual agent dynamics. In this paper, we employ a nonlinear time-varying coupling of diffusive type, which we call `edge-wise funnel coupling.' This idea is borrowed from adaptive control, which enables decentralized design of distributed optimizers without knowledge of global information. Remarkably, without a common internal model, each agent achieves asymptotic consensus to the optimal solution of the global cost. We illustrate this result by a network that asymptotically finds the least-squares solution of a linear equation in a distributed manner. |

Lee, Jin Gyu; Trenn, Stephan Asymptotic tracking via funnel control Inproceedings Proc. 58th IEEE Conf. Decision Control (CDC) 2019, Nice, France, 2019, (to appear). Abstract | Links | BibTeX | Tags: CDC, funnel-control, vidi @inproceedings{LeeTren19ppa, title = {Asymptotic tracking via funnel control}, author = {Jin Gyu Lee and Stephan Trenn}, url = {https://stephantrenn.net/wp-content/uploads/2019/03/Preprint-LT190910.pdf, Preprint}, year = {2019}, date = {2019-09-10}, booktitle = {Proc. 58th IEEE Conf. Decision Control (CDC) 2019}, address = {Nice, France}, abstract = {Funnel control is a powerful and simple method to solve the output tracking problem without the need of a good system model, without identification and without knowledge how the reference signal is produced, but transient behavior as well as arbitrary good accuracy can be guaranteed. Until recently, it was believed that the price to pay for these very nice properties is that only practical tracking and not asymptotic tracking can be achieved. Surprisingly, this is not true! We will prove that funnel control – without any further assumptions – can achieve asymptotic tracking.}, note = {to appear}, keywords = {CDC, funnel-control, vidi}, pubstate = {published}, tppubtype = {inproceedings} } Funnel control is a powerful and simple method to solve the output tracking problem without the need of a good system model, without identification and without knowledge how the reference signal is produced, but transient behavior as well as arbitrary good accuracy can be guaranteed. Until recently, it was believed that the price to pay for these very nice properties is that only practical tracking and not asymptotic tracking can be achieved. Surprisingly, this is not true! We will prove that funnel control – without any further assumptions – can achieve asymptotic tracking. |

Anh, Pham Ky; Linh, Pham Thi; Thuan, Do Duc; Trenn, Stephan The one-step-map for switched singular systems in discrete-time Inproceedings Proc. 58th IEEE Conf. Decision Control (CDC) 2019, Nice, France, 2019, (to appear). Abstract | Links | BibTeX | Tags: CDC, DAEs, solution-theory, switched-DAEs, switched-systems, vidi @inproceedings{AnhLinh19ppa, title = {The one-step-map for switched singular systems in discrete-time}, author = {Pham Ky Anh and Pham Thi Linh and Do Duc Thuan and Stephan Trenn}, url = {https://stephantrenn.net/wp-content/uploads/2019/03/Preprint-ALTT190910.pdf, Preprint}, year = {2019}, date = {2019-09-10}, booktitle = {Proc. 58th IEEE Conf. Decision Control (CDC) 2019}, address = {Nice, France}, abstract = {We study switched singular systems in discrete time and first highlight that in contrast to continuous time regularity of the corresponding matrix pairs is not sufficient to ensure a solution behavior which is causal with respect to the switching signal. With a suitable index-1 assumption for the whole switched system, we are able to define a one-step- map which can be used to provide explicit solution formulas for general switching signals.}, note = {to appear}, keywords = {CDC, DAEs, solution-theory, switched-DAEs, switched-systems, vidi}, pubstate = {published}, tppubtype = {inproceedings} } We study switched singular systems in discrete time and first highlight that in contrast to continuous time regularity of the corresponding matrix pairs is not sufficient to ensure a solution behavior which is causal with respect to the switching signal. With a suitable index-1 assumption for the whole switched system, we are able to define a one-step- map which can be used to provide explicit solution formulas for general switching signals. |

Trenn, Stephan; Unger, Benjamin Delay regularity of differential-algebraic equations Inproceedings Proc. 58th IEEE Conf. Decision Control (CDC) 2019, Nice, France, 2019, (to appear). Abstract | Links | BibTeX | Tags: CDC, DAEs, delay, solution-theory, vidi @inproceedings{TrenUnge19pp, title = {Delay regularity of differential-algebraic equations}, author = {Stephan Trenn and Benjamin Unger}, url = {https://stephantrenn.net/wp-content/uploads/2019/03/Preprint-TU190910.pdf, Preprint}, year = {2019}, date = {2019-09-10}, booktitle = {Proc. 58th IEEE Conf. Decision Control (CDC) 2019}, address = {Nice, France}, abstract = {We study linear time-invariant delay differential-algebraic equations (DDAEs). Such equations can arise if a feedback controller is applied to a descriptor system and the controller requires some time to measure the state and to compute the feedback resulting in the time-delay. We present an existence and uniqueness result for DDAEs within the space of piecewise-smooth distributions and an algorithm to determine whether a DDAE is delay-regular.}, note = {to appear}, keywords = {CDC, DAEs, delay, solution-theory, vidi}, pubstate = {published}, tppubtype = {inproceedings} } We study linear time-invariant delay differential-algebraic equations (DDAEs). Such equations can arise if a feedback controller is applied to a descriptor system and the controller requires some time to measure the state and to compute the feedback resulting in the time-delay. We present an existence and uniqueness result for DDAEs within the space of piecewise-smooth distributions and an algorithm to determine whether a DDAE is delay-regular. |

## 2017 |

Iervolino, Raffaele; Trenn, Stephan; Vasca, Francesco Stability of piecewise affine systems through discontinuous piecewise quadratic Lyapunov functions Inproceedings Proc. 56th IEEE Conf. Decis. Control, pp. 5894 - 5899, Melbourne, Australia, 2017. Abstract | Links | BibTeX | Tags: CDC, stability, switched-systems @inproceedings{IervTren17, title = {Stability of piecewise affine systems through discontinuous piecewise quadratic Lyapunov functions}, author = {Raffaele Iervolino and Stephan Trenn and Francesco Vasca}, url = {https://stephantrenn.net/wp-content/uploads/2017/09/Preprint-ITV170909.pdf, Preprint}, doi = {10.1109/CDC.2017.8264551}, year = {2017}, date = {2017-12-15}, booktitle = {Proc. 56th IEEE Conf. Decis. Control}, pages = {5894 - 5899}, address = {Melbourne, Australia}, abstract = {State-dependent switched systems characterized by piecewise affine (PWA) dynamics in a polyhedral partition of the state space are considered. Sufficient conditions on the vectors fields such that the solution crosses the common boundaries of the polyhedra are expressed in terms of quadratic inequalities constrained to the polyhedra intersections. A piece- wise quadratic (PWQ) function, not necessarily continuous, is proposed as a candidate Lyapunov function (LF). The sign conditions and the negative jumps at the boundaries are expressed in terms of linear matrix inequalities (LMIs) via cone- copositivity. A sufficient condition for the asymptotic stability of the PWA system is then obtained by finding a PWQ-LF through the solution of a set LMIs. Numerical results with a conewise linear system and an opinion dynamics model show the effectiveness of the proposed approach.}, keywords = {CDC, stability, switched-systems}, pubstate = {published}, tppubtype = {inproceedings} } State-dependent switched systems characterized by piecewise affine (PWA) dynamics in a polyhedral partition of the state space are considered. Sufficient conditions on the vectors fields such that the solution crosses the common boundaries of the polyhedra are expressed in terms of quadratic inequalities constrained to the polyhedra intersections. A piece- wise quadratic (PWQ) function, not necessarily continuous, is proposed as a candidate Lyapunov function (LF). The sign conditions and the negative jumps at the boundaries are expressed in terms of linear matrix inequalities (LMIs) via cone- copositivity. A sufficient condition for the asymptotic stability of the PWA system is then obtained by finding a PWQ-LF through the solution of a set LMIs. Numerical results with a conewise linear system and an opinion dynamics model show the effectiveness of the proposed approach. |

Kausar, Rukhsana; Trenn, Stephan Impulses in structured nonlinear switched DAEs Inproceedings Proc. 56th IEEE Conf. Decis. Control, pp. 3181 - 3186, Melbourne, Australia, 2017. Abstract | Links | BibTeX | Tags: application, CDC, DAEs, nonlinear, piecewise-smooth-distributions, solution-theory, switched-DAEs, switched-systems @inproceedings{KausTren17b, title = {Impulses in structured nonlinear switched DAEs}, author = {Rukhsana Kausar and Stephan Trenn}, url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-KT170920.pdf, Preprint}, doi = {10.1109/CDC.2017.8264125}, year = {2017}, date = {2017-12-14}, booktitle = {Proc. 56th IEEE Conf. Decis. Control}, pages = {3181 - 3186}, address = {Melbourne, Australia}, abstract = { Switched nonlinear differential algebraic equations (DAEs) occur in mathematical modeling of sudden transients in various physical phenomenons. Hence, it is important to investigate them with respect to the nature of their solutions. The few existing solvability results for switched nonlinear DAEs exclude Dirac impulses by definition; however, in many cases this is too restrictive. For example, in water distribution networks the water hammer effect can only be studied when allowing Dirac impulses in a nonlinear switched DAE description. We investigate existence and uniqueness of solutions with impulses for a general class of nonlinear switched DAEs, where we exploit a certain sparse structure of the nonlinearity.}, keywords = {application, CDC, DAEs, nonlinear, piecewise-smooth-distributions, solution-theory, switched-DAEs, switched-systems}, pubstate = {published}, tppubtype = {inproceedings} } Switched nonlinear differential algebraic equations (DAEs) occur in mathematical modeling of sudden transients in various physical phenomenons. Hence, it is important to investigate them with respect to the nature of their solutions. The few existing solvability results for switched nonlinear DAEs exclude Dirac impulses by definition; however, in many cases this is too restrictive. For example, in water distribution networks the water hammer effect can only be studied when allowing Dirac impulses in a nonlinear switched DAE description. We investigate existence and uniqueness of solutions with impulses for a general class of nonlinear switched DAEs, where we exploit a certain sparse structure of the nonlinearity. |

Küsters, Ferdinand; Patil, Deepak; Trenn, Stephan Switch observability for a class of inhomogeneous switched DAEs Inproceedings Proc. 56th IEEE Conf. Decis. Control, pp. 3175 - 3180, Melbourne, Australia, 2017. Abstract | Links | BibTeX | Tags: CDC, DAEs, observability, switched-DAEs, switched-systems @inproceedings{KustPati17b, title = {Switch observability for a class of inhomogeneous switched DAEs}, author = {Ferdinand Küsters and Deepak Patil and Stephan Trenn}, url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-KPT170919.pdf, Preprint}, doi = {10.1109/CDC.2017.8264124}, year = {2017}, date = {2017-12-13}, booktitle = {Proc. 56th IEEE Conf. Decis. Control}, pages = {3175 - 3180}, address = {Melbourne, Australia}, abstract = {Necessary and sufficient conditions for switching time and switch observability of a class of inhomogeneous switched differential algebraic equations (DAEs) are obtained. A characterization of initial states and inputs for which switched DAEs are switch unobservable is also provided by using the zeros of an augmented system obtained by combining the output of two modes suitably.}, keywords = {CDC, DAEs, observability, switched-DAEs, switched-systems}, pubstate = {published}, tppubtype = {inproceedings} } Necessary and sufficient conditions for switching time and switch observability of a class of inhomogeneous switched differential algebraic equations (DAEs) are obtained. A characterization of initial states and inputs for which switched DAEs are switch unobservable is also provided by using the zeros of an augmented system obtained by combining the output of two modes suitably. |

Küsters, Ferdinand; Trenn, Stephan; Wirsen, Andreas Switch-observer for switched linear systems Inproceedings Proc. 56th IEEE Conf. Decis. Control, pp. 1749 - 1754, Melbourne, Australia, 2017. Abstract | Links | BibTeX | Tags: CDC, observability, observer, switched-systems @inproceedings{KustTren17b, title = {Switch-observer for switched linear systems}, author = {Ferdinand Küsters and Stephan Trenn and Andreas Wirsen}, url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-KTW170901.pdf, Preprint}, doi = {10.1109/CDC.2017.8263903}, year = {2017}, date = {2017-12-12}, booktitle = {Proc. 56th IEEE Conf. Decis. Control}, pages = {1749 - 1754}, address = {Melbourne, Australia}, abstract = {To determine the switching signal and the state of a switched linear system, one usually requires mode observability. This requires that all individual modes are observable and that the modes are distinguishable. In theory, it allows to determine the active mode in an arbitrarily short time. If one enlarges the observation to an interval that contains a switch, both assumptions (observability of each mode and clearly distinct dynamics) can be relaxed. In [Küsters and Trenn 2017] this concept, called switch observability, was formalized. It is of particular interest for fault identification. Based on switch observability, we propose an observer. This observer combines the information obtained before and after a switching instant to determine both the state and the switching signal. It is analyzed and illustrated in an example.}, keywords = {CDC, observability, observer, switched-systems}, pubstate = {published}, tppubtype = {inproceedings} } To determine the switching signal and the state of a switched linear system, one usually requires mode observability. This requires that all individual modes are observable and that the modes are distinguishable. In theory, it allows to determine the active mode in an arbitrarily short time. If one enlarges the observation to an interval that contains a switch, both assumptions (observability of each mode and clearly distinct dynamics) can be relaxed. In [Küsters and Trenn 2017] this concept, called switch observability, was formalized. It is of particular interest for fault identification. Based on switch observability, we propose an observer. This observer combines the information obtained before and after a switching instant to determine both the state and the switching signal. It is analyzed and illustrated in an example. |

## 2016 |

Camlibel, Kanat; Iannelli, Luigi; Tanwani, Aneel; Trenn, Stephan Differential-algebraic inclusions with maximal monotone operators Inproceedings Proc. 55th IEEE Conf. Decis. Control, Las Vegas, USA, pp. 610–615, 2016. Abstract | Links | BibTeX | Tags: CDC, DAEs, nonlinear, solution-theory @inproceedings{CamlIann16, title = {Differential-algebraic inclusions with maximal monotone operators}, author = {Kanat Camlibel and Luigi Iannelli and Aneel Tanwani and Stephan Trenn}, url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-CITT160923.pdf, Preprint}, doi = {10.1109/CDC.2016.7798336}, year = {2016}, date = {2016-12-01}, booktitle = {Proc. 55th IEEE Conf. Decis. Control, Las Vegas, USA}, pages = {610--615}, abstract = {The term differential-algebraic inclusions (DAIs) not only describes the dynamical relations using set-valued mappings, but also includes the static algebraic inclusions, and this paper considers the problem of existence of solutions for a class of such dynamical systems described by the inclusion ddt Px in -M(x) for a symmetric positive semi-definite matrix P in R^(n x n), and a maximal monotone operator M:R^n => R^n. The existence of solutions is proved using the tools from the theory of maximal monotone operators. The class of solutions that we study in the paper have the property that, instead of the whole state, only Px is absolutely continuous and unique. This framework, in particular, is useful for studying passive differential-algebraic equations (DAEs) coupled with maximal monotone relations. Certain class of irregular DAEs are also covered within the proposed general framework. Applications from electrical circuits are included to provide a practical motivation.}, keywords = {CDC, DAEs, nonlinear, solution-theory}, pubstate = {published}, tppubtype = {inproceedings} } The term differential-algebraic inclusions (DAIs) not only describes the dynamical relations using set-valued mappings, but also includes the static algebraic inclusions, and this paper considers the problem of existence of solutions for a class of such dynamical systems described by the inclusion ddt Px in -M(x) for a symmetric positive semi-definite matrix P in R^(n x n), and a maximal monotone operator M:R^n => R^n. The existence of solutions is proved using the tools from the theory of maximal monotone operators. The class of solutions that we study in the paper have the property that, instead of the whole state, only Px is absolutely continuous and unique. This framework, in particular, is useful for studying passive differential-algebraic equations (DAEs) coupled with maximal monotone relations. Certain class of irregular DAEs are also covered within the proposed general framework. Applications from electrical circuits are included to provide a practical motivation. |

## 2015 |

Küsters, Ferdinand; Trenn, Stephan Duality of switched ODEs with jumps Inproceedings Proc. 54th IEEE Conf. Decis. Control, Osaka, Japan, pp. 4879–4884, 2015. Abstract | Links | BibTeX | Tags: CDC, controllability, observability, switched-systems @inproceedings{KustTren15b, title = {Duality of switched ODEs with jumps}, author = {Ferdinand Küsters and Stephan Trenn}, url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-KT150814.pdf, Preprint}, doi = {10.1109/CDC.2015.7402981}, year = {2015}, date = {2015-12-05}, booktitle = {Proc. 54th IEEE Conf. Decis. Control, Osaka, Japan}, pages = {4879--4884}, abstract = {Duality between controllability/reachability and determinability/observability of switched systems with jumps is proven. The duality result is based on the recent characterization of controllability for switched differential-algebraic equations (DAEs) which share many properties with switched ordinary differential equations (ODEs) with jumps. Here we view the switching signal as given and fixed, which makes the overall switched system time-varying, in particular controllability and reachability do not coincide anymore.}, keywords = {CDC, controllability, observability, switched-systems}, pubstate = {published}, tppubtype = {inproceedings} } Duality between controllability/reachability and determinability/observability of switched systems with jumps is proven. The duality result is based on the recent characterization of controllability for switched differential-algebraic equations (DAEs) which share many properties with switched ordinary differential equations (ODEs) with jumps. Here we view the switching signal as given and fixed, which makes the overall switched system time-varying, in particular controllability and reachability do not coincide anymore. |

Trenn, Stephan Distributional averaging of switched DAEs with two modes Inproceedings Proc. 54th IEEE Conf. Decis. Control, Osaka, Japan, pp. 3616–3620, 2015. Abstract | Links | BibTeX | Tags: averaging, CDC, DAEs, piecewise-smooth-distributions, switched-DAEs, switched-systems @inproceedings{Tren15, title = {Distributional averaging of switched DAEs with two modes}, author = {Stephan Trenn}, url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-Tre150812.pdf, Preprint}, doi = {10.1109/CDC.2015.7402779}, year = {2015}, date = {2015-12-04}, booktitle = {Proc. 54th IEEE Conf. Decis. Control, Osaka, Japan}, pages = {3616--3620}, abstract = {The averaging technique is a powerful tool for the analysis and control of switched systems. Recently, classical averaging results were generalized to the class of switched differential algebraic equations (switched DAEs). These results did not consider the possible Dirac impulses in the solutions of switched DAEs and it was believed that the presence of Dirac impulses does not prevent convergence towards an average model and can therefore be neglected. It turns out that the first claim (convergence) is indeed true, but nevertheless the Dirac impulses cannot be neglected, they play an important role for the resulting limit. This note first shows with a simple example how the presence of Dirac impulses effects the convergence towards an averaged model and then a formal proof of convergence in the distributional sense for switched DAEs with two modes is given.}, keywords = {averaging, CDC, DAEs, piecewise-smooth-distributions, switched-DAEs, switched-systems}, pubstate = {published}, tppubtype = {inproceedings} } The averaging technique is a powerful tool for the analysis and control of switched systems. Recently, classical averaging results were generalized to the class of switched differential algebraic equations (switched DAEs). These results did not consider the possible Dirac impulses in the solutions of switched DAEs and it was believed that the presence of Dirac impulses does not prevent convergence towards an average model and can therefore be neglected. It turns out that the first claim (convergence) is indeed true, but nevertheless the Dirac impulses cannot be neglected, they play an important role for the resulting limit. This note first shows with a simple example how the presence of Dirac impulses effects the convergence towards an averaged model and then a formal proof of convergence in the distributional sense for switched DAEs with two modes is given. |

Tanwani, Aneel; Trenn, Stephan On detectability of switched linear differential-algebraic equations Inproceedings Proc. 54th IEEE Conf. Decis. Control, Osaka, Japan, pp. 2957–2962, 2015. Abstract | Links | BibTeX | Tags: CDC, DAEs, observability, stability, switched-DAEs, switched-systems @inproceedings{TanwTren15, title = {On detectability of switched linear differential-algebraic equations}, author = {Aneel Tanwani and Stephan Trenn}, url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-TT150904.pdf, Preprint}, doi = {10.1109/CDC.2015.7402666}, year = {2015}, date = {2015-12-03}, booktitle = {Proc. 54th IEEE Conf. Decis. Control, Osaka, Japan}, pages = {2957--2962}, abstract = {This paper addresses the notion of detectability for continuous-time switched systems comprising linear differential-algebraic equations (DAEs). It relates to studying asymptotic stability of the set of state trajectories corresponding to zero input and zero output, with a fixed switching signal. Due to the nature of solutions of switched DAEs, the problem reduces to analyzing stability of the trajectories emanating from a non-vanishing unobservable subspace, for which we first derive a geometric expression. The stability of state trajectories starting from that subspace can then be checked in two possible ways. In the first case, detectability of switched DAE is shown to be equivalent to the asymptotic stability of a reduced order discrete-time switched system. In the second approach, the solutions from a non-vanishing unobservable subspace are mapped to the solutions of a reduced order continuous system with time-varying switching ordinary differential equations (ODEs). As a special case of the later approach, the reduced order switched system is time-invariant if the unobservable subspace is invariant for all subsystems}, keywords = {CDC, DAEs, observability, stability, switched-DAEs, switched-systems}, pubstate = {published}, tppubtype = {inproceedings} } This paper addresses the notion of detectability for continuous-time switched systems comprising linear differential-algebraic equations (DAEs). It relates to studying asymptotic stability of the set of state trajectories corresponding to zero input and zero output, with a fixed switching signal. Due to the nature of solutions of switched DAEs, the problem reduces to analyzing stability of the trajectories emanating from a non-vanishing unobservable subspace, for which we first derive a geometric expression. The stability of state trajectories starting from that subspace can then be checked in two possible ways. In the first case, detectability of switched DAE is shown to be equivalent to the asymptotic stability of a reduced order discrete-time switched system. In the second approach, the solutions from a non-vanishing unobservable subspace are mapped to the solutions of a reduced order continuous system with time-varying switching ordinary differential equations (ODEs). As a special case of the later approach, the reduced order switched system is time-invariant if the unobservable subspace is invariant for all subsystems |

Mostacciuolo, Elisa; Trenn, Stephan; Vasca, Francesco Averaging for non-homogeneous switched DAEs Inproceedings Proc. 54th IEEE Conf. Decis. Control, Osaka, Japan, pp. 2951–2956, 2015. Abstract | Links | BibTeX | Tags: application, averaging, CDC, DAEs, switched-DAEs, switched-systems @inproceedings{MostTren15b, title = {Averaging for non-homogeneous switched DAEs}, author = {Elisa Mostacciuolo and Stephan Trenn and Francesco Vasca}, url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-MTV150901.pdf, Preprint}, doi = {10.1109/CDC.2015.7402665}, year = {2015}, date = {2015-12-02}, booktitle = {Proc. 54th IEEE Conf. Decis. Control, Osaka, Japan}, pages = {2951--2956}, abstract = {Averaging is widely used for approximating the dynamics of switched systems. The validity of an averaged model typically depends on the switching frequency and on some technicalities regarding the switched system structure. For homogeneous linear switched differential algebraic equations it is known that an averaged model can be obtained. In this paper an averaging result for non-homogeneous switched systems is presented. A switched electrical circuit illustrates the practical interest of the result.}, keywords = {application, averaging, CDC, DAEs, switched-DAEs, switched-systems}, pubstate = {published}, tppubtype = {inproceedings} } Averaging is widely used for approximating the dynamics of switched systems. The validity of an averaged model typically depends on the switching frequency and on some technicalities regarding the switched system structure. For homogeneous linear switched differential algebraic equations it is known that an averaged model can be obtained. In this paper an averaging result for non-homogeneous switched systems is presented. A switched electrical circuit illustrates the practical interest of the result. |

Shim, Hyungbo; Trenn, Stephan A preliminary result on synchronization of heterogeneous agents via funnel control Inproceedings Proc. 54th IEEE Conf. Decis. Control, Osaka, Japan, pp. 2229–2234, 2015. Abstract | Links | BibTeX | Tags: CDC, funnel-control, networks, nonlinear, stability, synchronization @inproceedings{ShimTren15, title = {A preliminary result on synchronization of heterogeneous agents via funnel control}, author = {Hyungbo Shim and Stephan Trenn}, url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-ST150902.pdf, Preprint}, doi = {10.1109/CDC.2015.7402538}, year = {2015}, date = {2015-12-01}, booktitle = {Proc. 54th IEEE Conf. Decis. Control, Osaka, Japan}, pages = {2229--2234}, abstract = {We propose a new approach to achieve practical synchronization for heterogeneous agents. Our approach is based on the observation that a sufficiently large (but constant) gain for diffusive coupling leads to practical synchronization. In the classical setup of high-gain adaptive control, the funnel controller gained popularity in the last decade, because it is very simple and only structural knowledge of the underlying dynamical system is needed. We illustrate with simulations that “funnel synchronization” may be a promising approach to achieve practical synchronization of heterogeneous agents without the need to know the individual dynamics and the algebraic connectivity of the network (i.e., the second smallest eigenvalue of the Laplacian matrix). For a special case we provide a proof, but the proof for the general case is ongoing research.}, keywords = {CDC, funnel-control, networks, nonlinear, stability, synchronization}, pubstate = {published}, tppubtype = {inproceedings} } We propose a new approach to achieve practical synchronization for heterogeneous agents. Our approach is based on the observation that a sufficiently large (but constant) gain for diffusive coupling leads to practical synchronization. In the classical setup of high-gain adaptive control, the funnel controller gained popularity in the last decade, because it is very simple and only structural knowledge of the underlying dynamical system is needed. We illustrate with simulations that “funnel synchronization” may be a promising approach to achieve practical synchronization of heterogeneous agents without the need to know the individual dynamics and the algebraic connectivity of the network (i.e., the second smallest eigenvalue of the Laplacian matrix). For a special case we provide a proof, but the proof for the general case is ongoing research. |

## 2013 |

Tanwani, Aneel; Trenn, Stephan An observer for switched differential-algebraic equations based on geometric characterization of observability Inproceedings Proc. 52nd IEEE Conf. Decis. Control, Florence, Italy, pp. 5981–5986, 2013. Abstract | Links | BibTeX | Tags: CDC, DAEs, observability, observer, piecewise-smooth-distributions, switched-DAEs, switched-systems @inproceedings{TanwTren13, title = {An observer for switched differential-algebraic equations based on geometric characterization of observability}, author = {Aneel Tanwani and Stephan Trenn}, url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-TT130909.pdf, Preprint}, doi = {10.1109/CDC.2013.6760833}, year = {2013}, date = {2013-12-12}, booktitle = {Proc. 52nd IEEE Conf. Decis. Control, Florence, Italy}, pages = {5981--5986}, abstract = {Based on our previous work dealing with geometric characterization of observability for switched differential-algebraic equations (switched DAEs), we propose an observer design for switched DAEs that generates an asymptotically convergent state estimate. Without assuming the observability of individual modes, the central idea in constructing the observer is to filter out the maximal information from the output of each of the active subsystems and combine it with the previously extracted information to obtain a good estimate of the state after a certain time has passed. In general, observability only holds when impulses in the output are taken into account, hence our observer incorporates the knowledge of impulses in the output. This is a distinguishing feature of our observer design compared to observers for switched ordinary differential equations.}, keywords = {CDC, DAEs, observability, observer, piecewise-smooth-distributions, switched-DAEs, switched-systems}, pubstate = {published}, tppubtype = {inproceedings} } Based on our previous work dealing with geometric characterization of observability for switched differential-algebraic equations (switched DAEs), we propose an observer design for switched DAEs that generates an asymptotically convergent state estimate. Without assuming the observability of individual modes, the central idea in constructing the observer is to filter out the maximal information from the output of each of the active subsystems and combine it with the previously extracted information to obtain a good estimate of the state after a certain time has passed. In general, observability only holds when impulses in the output are taken into account, hence our observer incorporates the knowledge of impulses in the output. This is a distinguishing feature of our observer design compared to observers for switched ordinary differential equations. |

Costantini, Giuliano; Trenn, Stephan; Vasca, Francesco Regularity and passivity for jump rules in linear switched systems Inproceedings Proc. 52nd IEEE Conf. Decis. Control, Florence, Italy, pp. 4030–4035, 2013, ISSN: 0191-2216. Abstract | Links | BibTeX | Tags: CDC, DAEs, solution-theory, switched-DAEs, switched-systems @inproceedings{CostTren13, title = {Regularity and passivity for jump rules in linear switched systems}, author = {Giuliano Costantini and Stephan Trenn and Francesco Vasca}, url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-CTV130906.pdf, Preprint}, doi = {10.1109/CDC.2013.6760506}, issn = {0191-2216}, year = {2013}, date = {2013-12-11}, booktitle = {Proc. 52nd IEEE Conf. Decis. Control, Florence, Italy}, pages = {4030--4035}, abstract = {A wide class of linear switched systems (LSS) can be represented by a sequence of modes each one described by a set of differential algebraic equations (DAEs). LSS can exhibit discontinuities in the state evolution, also called jumps, when the state at the end of a mode is not consistent with the DAEs of the successive mode. Then the problem of defining a proper state jump rule arises when an inconsistent initial condition is given. Regularity and passivity conditions provide two conceptually different jump maps respectively. In this paper, after proving some preliminary result on the jump analysis within the regularity framework, it is shown the equivalence of regularity-based and passivity-based jump rules. A switched capacitor electrical circuit is used to numerically confirm the theoretical result.}, keywords = {CDC, DAEs, solution-theory, switched-DAEs, switched-systems}, pubstate = {published}, tppubtype = {inproceedings} } A wide class of linear switched systems (LSS) can be represented by a sequence of modes each one described by a set of differential algebraic equations (DAEs). LSS can exhibit discontinuities in the state evolution, also called jumps, when the state at the end of a mode is not consistent with the DAEs of the successive mode. Then the problem of defining a proper state jump rule arises when an inconsistent initial condition is given. Regularity and passivity conditions provide two conceptually different jump maps respectively. In this paper, after proving some preliminary result on the jump analysis within the regularity framework, it is shown the equivalence of regularity-based and passivity-based jump rules. A switched capacitor electrical circuit is used to numerically confirm the theoretical result. |

Iannelli, Luigi; Pedicini, Carmen; Trenn, Stephan; Vasca, Francesco An averaging result for switched DAEs with multiple modes Inproceedings Proc. 52nd IEEE Conf. Decis. Control, Florence, Italy, pp. 1378 - 1383, 2013. Abstract | Links | BibTeX | Tags: averaging, CDC, DAEs, switched-DAEs, switched-systems @inproceedings{IannPedi13b, title = {An averaging result for switched DAEs with multiple modes}, author = {Luigi Iannelli and Carmen Pedicini and Stephan Trenn and Francesco Vasca}, url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-IPTV130911.pdf, Preprint}, doi = {10.1109/CDC.2013.6760075}, year = {2013}, date = {2013-12-10}, booktitle = {Proc. 52nd IEEE Conf. Decis. Control, Florence, Italy}, pages = {1378 - 1383}, abstract = {The major motivation of the averaging technique for switched systems is the construction of a smooth average system whose state trajectory approximates in some sense the state trajectory of the switched system. Averaging of dynamic systems represented by switched ordinary differential equations (ODEs) has been widely analyzed in the literature. The averaging approach can be useful also for the analysis of switched differential algebraic equations (DAEs). Indeed by analyzing the evolution of the switched DAEs state it is possible to conjecture the existence of an average model. However a trivial generalization of the ODE case is not possible due to the presence of state jumps. In this paper we discuss the averaging approach for switched DAEs and an approximation result is derived for homogenous switched linear DAE with periodic switching signals commuting among several modes. This approximation result extends a recent averaging result for switched DAEs with only two modes. Numerical simulations confirm the validity of the averaging approach for switched DAEs.}, keywords = {averaging, CDC, DAEs, switched-DAEs, switched-systems}, pubstate = {published}, tppubtype = {inproceedings} } The major motivation of the averaging technique for switched systems is the construction of a smooth average system whose state trajectory approximates in some sense the state trajectory of the switched system. Averaging of dynamic systems represented by switched ordinary differential equations (ODEs) has been widely analyzed in the literature. The averaging approach can be useful also for the analysis of switched differential algebraic equations (DAEs). Indeed by analyzing the evolution of the switched DAEs state it is possible to conjecture the existence of an average model. However a trivial generalization of the ODE case is not possible due to the presence of state jumps. In this paper we discuss the averaging approach for switched DAEs and an approximation result is derived for homogenous switched linear DAE with periodic switching signals commuting among several modes. This approximation result extends a recent averaging result for switched DAEs with only two modes. Numerical simulations confirm the validity of the averaging approach for switched DAEs. |

## 2012 |

Trenn, Stephan; Willems, Jan C Switched behaviors with impulses - a unifying framework Inproceedings Proc. 51st IEEE Conf. Decis. Control, Maui, USA, pp. 3203-3208, 2012, ISSN: 0743-1546. Abstract | Links | BibTeX | Tags: CDC, DAEs, piecewise-smooth-distributions, switched-DAEs, switched-systems @inproceedings{TrenWill12, title = {Switched behaviors with impulses - a unifying framework}, author = {Stephan Trenn and Jan C. Willems}, url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-TW120813.pdf, Preprint}, doi = {10.1109/CDC.2012.6426883}, issn = {0743-1546}, year = {2012}, date = {2012-12-13}, booktitle = {Proc. 51st IEEE Conf. Decis. Control, Maui, USA}, pages = {3203-3208}, abstract = {We present a new framework to describe and study switched behaviors. We allow for jumps and impulses in the trajectories induced either implicitly by the dynamics after the switch or explicitly by “impacts”. With some examples from electrical circuit we motivate that the dynamical equations before and after the switch already uniquely define the “dynamics” at the switch, i.e. jumps and impulses. On the other hand, we also allow for external impacts resulting in jumps and impulses not induced by the internal dynamics. As a first theoretical result in this new framework we present a characterization for autonomy of a switched behavior.}, keywords = {CDC, DAEs, piecewise-smooth-distributions, switched-DAEs, switched-systems}, pubstate = {published}, tppubtype = {inproceedings} } We present a new framework to describe and study switched behaviors. We allow for jumps and impulses in the trajectories induced either implicitly by the dynamics after the switch or explicitly by “impacts”. With some examples from electrical circuit we motivate that the dynamical equations before and after the switch already uniquely define the “dynamics” at the switch, i.e. jumps and impulses. On the other hand, we also allow for external impacts resulting in jumps and impulses not induced by the internal dynamics. As a first theoretical result in this new framework we present a characterization for autonomy of a switched behavior. |

Trenn, Stephan; Wirth, Fabian Linear switched DAEs: Lyapunov exponents, a converse Lyapunov theorem, and Barabanov norms Inproceedings Proc. 51st IEEE Conf. Decis. Control, Maui, USA, pp. 2666–2671, 2012, ISSN: 0191-2216. Abstract | Links | BibTeX | Tags: CDC, DAEs, Lyapunov, stability, switched-DAEs, switched-systems @inproceedings{TrenWirt12b, title = {Linear switched DAEs: Lyapunov exponents, a converse Lyapunov theorem, and Barabanov norms}, author = {Stephan Trenn and Fabian Wirth}, url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-TW120901.pdf, Preprint}, doi = {10.1109/CDC.2012.6426245}, issn = {0191-2216}, year = {2012}, date = {2012-12-12}, booktitle = {Proc. 51st IEEE Conf. Decis. Control, Maui, USA}, pages = {2666--2671}, abstract = {For linear switched differential algebraic equations (DAEs) we consider the problem of characterizing the maximal exponential growth rate of solutions. It is shown that a finite exponential growth rate exists if and only if the set of consistency projectors associated to the family of DAEs is product bounded. This result may be used to derive a converse Lyapunov theorem for switched DAEs. Under the assumption of irreducibility we show that a construction reminiscent of the construction of Barabanov norms is feasible as well.}, keywords = {CDC, DAEs, Lyapunov, stability, switched-DAEs, switched-systems}, pubstate = {published}, tppubtype = {inproceedings} } For linear switched differential algebraic equations (DAEs) we consider the problem of characterizing the maximal exponential growth rate of solutions. It is shown that a finite exponential growth rate exists if and only if the set of consistency projectors associated to the family of DAEs is product bounded. This result may be used to derive a converse Lyapunov theorem for switched DAEs. Under the assumption of irreducibility we show that a construction reminiscent of the construction of Barabanov norms is feasible as well. |

Tanwani, Aneel; Trenn, Stephan Observability of switched differential-algebraic equations for general switching signals Inproceedings Proc. 51st IEEE Conf. Decis. Control, Maui, USA, pp. 2648–2653, 2012. Abstract | Links | BibTeX | Tags: CDC, DAEs, observability, switched-DAEs, switched-systems @inproceedings{TanwTren12, title = {Observability of switched differential-algebraic equations for general switching signals}, author = {Aneel Tanwani and Stephan Trenn}, url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-TT120822.pdf, Preprint}, doi = {10.1109/CDC.2012.6427087}, year = {2012}, date = {2012-12-11}, booktitle = {Proc. 51st IEEE Conf. Decis. Control, Maui, USA}, pages = {2648--2653}, abstract = {We study observability of switched differential-algebraic equations (DAEs) for arbitrary switching. We present a characterization of observability and a related property called determinability. These characterizations utilize the results for the single-switch case recently obtained by the authors. Furthermore, we study observability conditions when only the mode sequence of the switching signal (and not the switching times) are known. This leads to necessary and sufficient conditions for observability and determinability. We illustrate the results with illustrative examples.}, keywords = {CDC, DAEs, observability, switched-DAEs, switched-systems}, pubstate = {published}, tppubtype = {inproceedings} } We study observability of switched differential-algebraic equations (DAEs) for arbitrary switching. We present a characterization of observability and a related property called determinability. These characterizations utilize the results for the single-switch case recently obtained by the authors. Furthermore, we study observability conditions when only the mode sequence of the switching signal (and not the switching times) are known. This leads to necessary and sufficient conditions for observability and determinability. We illustrate the results with illustrative examples. |

## 2011 |

Liberzon, Daniel; Trenn, Stephan; Wirth, Fabian Commutativity and asymptotic stability for linear switched DAEs Inproceedings Proc. 50th IEEE Conf. Decis. Control and European Control Conf. ECC 2011, Orlando, USA, pp. 417–422, 2011. Abstract | Links | BibTeX | Tags: CDC, DAEs, Lyapunov, stability, switched-DAEs, switched-systems @inproceedings{LibeTren11, title = {Commutativity and asymptotic stability for linear switched DAEs}, author = {Daniel Liberzon and Stephan Trenn and Fabian Wirth}, url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-LTW110816.pdf, Preprint}, doi = {10.1109/CDC.2011.6160335}, year = {2011}, date = {2011-12-01}, booktitle = {Proc. 50th IEEE Conf. Decis. Control and European Control Conf. ECC 2011, Orlando, USA}, pages = {417--422}, abstract = {For linear switched ordinary differential equations with asymptotically stable constituent systems, it is well known that commutativity of the coefficient matrices implies asymptotic stability of the switched system under arbitrary switching. This result is generalized to linear switched differential algebraic equations (DAEs). Although the solutions of a switched DAE can exhibit jumps it turns out that it suffices to check commutativity of the “flow” matrices. As in the ODE case we are also able to construct a common quadratic Lyapunov function.}, keywords = {CDC, DAEs, Lyapunov, stability, switched-DAEs, switched-systems}, pubstate = {published}, tppubtype = {inproceedings} } For linear switched ordinary differential equations with asymptotically stable constituent systems, it is well known that commutativity of the coefficient matrices implies asymptotic stability of the switched system under arbitrary switching. This result is generalized to linear switched differential algebraic equations (DAEs). Although the solutions of a switched DAE can exhibit jumps it turns out that it suffices to check commutativity of the “flow” matrices. As in the ODE case we are also able to construct a common quadratic Lyapunov function. |

## 2010 |

Domínguez-García, Alejandro D; Trenn, Stephan Detection of impulsive effects in switched DAEs with applications to power electronics reliability analysis Inproceedings Proc. 49th IEEE Conf. Decis. Control, Atlanta, USA, pp. 5662–5667, 2010. Abstract | Links | BibTeX | Tags: application, CDC, DAEs, piecewise-smooth-distributions, switched-DAEs, switched-systems @inproceedings{DomiTren10, title = {Detection of impulsive effects in switched DAEs with applications to power electronics reliability analysis}, author = {Alejandro D. Domínguez-García and Stephan Trenn}, url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-DT100810.pdf, Preprint}, doi = {10.1109/CDC.2010.5717011}, year = {2010}, date = {2010-12-17}, booktitle = {Proc. 49th IEEE Conf. Decis. Control, Atlanta, USA}, pages = {5662--5667}, abstract = {This paper presents an analytical framework for detecting the presence of jumps and impulses in the solutions of switched differential algebraic equations (switched DAEs). The framework can be applied in the early design stage of fault-tolerant power electronics systems to identify design flaws that could jeopardize its reliability. The system is described by a switched differential algebraic equation, accounting for both fault-free system configurations and the configurations that arise after component faults, where each configuration p is defined by a pair of matrices (Ep;Ap). For each configuration p, the so called consistency projector is obtained from the pair (Ep;Ap). Based on the consistency projectors of all possible configurations, conditions for impulse-free and jump-free solutions of the switched DAE are established. A case-study of a dual redundant buck converter is presented to illustrate the framework.}, keywords = {application, CDC, DAEs, piecewise-smooth-distributions, switched-DAEs, switched-systems}, pubstate = {published}, tppubtype = {inproceedings} } This paper presents an analytical framework for detecting the presence of jumps and impulses in the solutions of switched differential algebraic equations (switched DAEs). The framework can be applied in the early design stage of fault-tolerant power electronics systems to identify design flaws that could jeopardize its reliability. The system is described by a switched differential algebraic equation, accounting for both fault-free system configurations and the configurations that arise after component faults, where each configuration p is defined by a pair of matrices (Ep;Ap). For each configuration p, the so called consistency projector is obtained from the pair (Ep;Ap). Based on the consistency projectors of all possible configurations, conditions for impulse-free and jump-free solutions of the switched DAE are established. A case-study of a dual redundant buck converter is presented to illustrate the framework. |

Tanwani, Aneel; Trenn, Stephan On observability of switched differential-algebraic equations Inproceedings Proc. 49th IEEE Conf. Decis. Control, Atlanta, USA, pp. 5656–5661, 2010. Abstract | Links | BibTeX | Tags: CDC, DAEs, observability, piecewise-smooth-distributions, switched-DAEs, switched-systems @inproceedings{TanwTren10, title = {On observability of switched differential-algebraic equations}, author = {Aneel Tanwani and Stephan Trenn}, url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-TT100821.pdf, Preprint}, doi = {10.1109/CDC.2010.5717685}, year = {2010}, date = {2010-12-16}, booktitle = {Proc. 49th IEEE Conf. Decis. Control, Atlanta, USA}, pages = {5656--5661}, abstract = {We investigate observability of switched differential algebraic equations. The article primarily focuses on a class of switched systems comprising of two modes and a switching signal with a single switching instant. We provide a necessary and sufficient condition under which it is possible to recover the value of state trajectory (globally in time) with the help of switching phenomenon, even though the constituent subsystems may not be observable. In case the switched system is not globally observable, we discuss the concept of forward observability which deals with the recovery of state trajectory after the switching. A necessary and sufficient condition that characterizes forward observability is presented.}, keywords = {CDC, DAEs, observability, piecewise-smooth-distributions, switched-DAEs, switched-systems}, pubstate = {published}, tppubtype = {inproceedings} } We investigate observability of switched differential algebraic equations. The article primarily focuses on a class of switched systems comprising of two modes and a switching signal with a single switching instant. We provide a necessary and sufficient condition under which it is possible to recover the value of state trajectory (globally in time) with the help of switching phenomenon, even though the constituent subsystems may not be observable. In case the switched system is not globally observable, we discuss the concept of forward observability which deals with the recovery of state trajectory after the switching. A necessary and sufficient condition that characterizes forward observability is presented. |

Liberzon, Daniel; Trenn, Stephan The bang-bang funnel controller Inproceedings Proc. 49th IEEE Conf. Decis. Control, Atlanta, USA, pp. 690–695, 2010. Abstract | Links | BibTeX | Tags: CDC, funnel-control, input-constraints, nonlinear, relative-degree @inproceedings{LibeTren10, title = {The bang-bang funnel controller}, author = {Daniel Liberzon and Stephan Trenn}, url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-LT100806.pdf, Preprint http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-LT100806longVersion.pdf, Preprint (long version)}, doi = {10.1109/CDC.2010.5717742}, year = {2010}, date = {2010-12-15}, booktitle = {Proc. 49th IEEE Conf. Decis. Control, Atlanta, USA}, pages = {690--695}, abstract = {A bang-bang controller is proposed which is able to ensure reference signal tracking with prespecified time-varying error bounds (the funnel) for nonlinear systems with relative degree one or two. For the design of the controller only the knowledge of the relative degree is needed. The controller is guaranteed to work when certain feasibility assumptions are fulfilled, which are explicitly given in the main results. Linear systems with relative degree one or two are feasible if the system is minimum phase and the control values are large enough.}, keywords = {CDC, funnel-control, input-constraints, nonlinear, relative-degree}, pubstate = {published}, tppubtype = {inproceedings} } A bang-bang controller is proposed which is able to ensure reference signal tracking with prespecified time-varying error bounds (the funnel) for nonlinear systems with relative degree one or two. For the design of the controller only the knowledge of the relative degree is needed. The controller is guaranteed to work when certain feasibility assumptions are fulfilled, which are explicitly given in the main results. Linear systems with relative degree one or two are feasible if the system is minimum phase and the control values are large enough. |

## 2009 |

Liberzon, Daniel; Trenn, Stephan On stability of linear switched differential algebraic equations Inproceedings Proc. Joint 48th IEEE Conf. Decis. Control and 28th Chinese Control Conf., pp. 2156–2161, 2009. Abstract | Links | BibTeX | Tags: CDC, DAEs, Lyapunov, stability, switched-DAEs, switched-systems @inproceedings{LibeTren09, title = {On stability of linear switched differential algebraic equations}, author = {Daniel Liberzon and Stephan Trenn}, url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-LT090903.pdf, Preprint}, doi = {10.1109/CDC.2009.5400076}, year = {2009}, date = {2009-12-01}, booktitle = {Proc. Joint 48th IEEE Conf. Decis. Control and 28th Chinese Control Conf.}, pages = {2156--2161}, abstract = {This paper studies linear switched differential algebraic equations (DAEs), i.e., systems defined by a finite family of linear DAE subsystems and a switching signal that governs the switching between them. We show by examples that switching between stable subsystems may lead to instability, and that the presence of algebraic constraints leads to a larger variety of possible instability mechanisms compared to those observed in switched systems described by ordinary differential equations (ODEs). We prove two sufficient conditions for stability of switched DAEs based on the existence of suitable Lyapunov functions. The first result states that a common Lyapunov function guarantees stability under arbitrary switching when an additional condition involving consistency projectors holds (this extra condition is not needed when there are no jumps, as in the case of switched ODEs). The second result shows that stability is preserved under switching with sufficiently large dwell time.}, keywords = {CDC, DAEs, Lyapunov, stability, switched-DAEs, switched-systems}, pubstate = {published}, tppubtype = {inproceedings} } This paper studies linear switched differential algebraic equations (DAEs), i.e., systems defined by a finite family of linear DAE subsystems and a switching signal that governs the switching between them. We show by examples that switching between stable subsystems may lead to instability, and that the presence of algebraic constraints leads to a larger variety of possible instability mechanisms compared to those observed in switched systems described by ordinary differential equations (ODEs). We prove two sufficient conditions for stability of switched DAEs based on the existence of suitable Lyapunov functions. The first result states that a common Lyapunov function guarantees stability under arbitrary switching when an additional condition involving consistency projectors holds (this extra condition is not needed when there are no jumps, as in the case of switched ODEs). The second result shows that stability is preserved under switching with sufficiently large dwell time. |

## 2005 |

French, Mark; Trenn, Stephan l Proc. 44th IEEE Conf. Decis. Control and European Control Conf. (ECC), pp. 2865–2870, 2005. Abstract | Links | BibTeX | Tags: CDC, stability, switched-systems @inproceedings{FrenTren05, title = {l^{p} gain bounds for switched adaptive controllers}, author = {Mark French and Stephan Trenn}, url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-FT050913.pdf, Preprint}, doi = {10.1109/CDC.2005.1582598}, year = {2005}, date = {2005-12-01}, booktitle = {Proc. 44th IEEE Conf. Decis. Control and European Control Conf. (ECC)}, pages = {2865--2870}, abstract = {A class of discrete plants controlled by a switching adaptive strategy is considered, and l^p bounds, 1 ≤ p ≤ ∞, are obtained for the closed loop gain relating input and output disturbances to internal signals.}, keywords = {CDC, stability, switched-systems}, pubstate = {published}, tppubtype = {inproceedings} } A class of discrete plants controlled by a switching adaptive strategy is considered, and l^p bounds, 1 ≤ p ≤ ∞, are obtained for the closed loop gain relating input and output disturbances to internal signals. |