Publications

@inproceedings{ChenTren24,

title = {Solution concepts for linear piecewise affine differential-algebraic equations},

author = {Yahao Chen and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2024/09/Preprint-CT240911.pdf, Preprint},

year  = {2024},

date = {2024-12-16},

urldate = {2024-12-16},

booktitle = {Proc. 63rd IEEE Conf. Decision Control (CDC 2024)},

address = {Milan, Italy},

organization = {IEEE},

abstract = {In this paper, we introduce a definition of solu- tions for linear piecewise affine differential-algebraic equations (PWA-DAEs). Firstly, to address the conflict between projector-based jump rule and active regions, we propose a concept called state-dependent jump path. Unlike the conventional perspective that treats jumps as discrete-time dynamics, we interpret them as continuous dynamics, parameterized by a virtual time-variable. Secondly, by adapting the hybrid time-domain solution theory for continuous-discrete hybrid systems, we define the concept of jump-flow solutions for PWA-DAEs with the help of Filippov solutions for differential inclusions. Subsequently, we study various boundary behaviors of jump-flow solutions. Finally, we apply the proposed solution concepts in simulating a state-dependent switching circuit.},

note = {to appear},

keywords = {DAEs, piecewise-smooth-distributions, solution-theory, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{ChanTren23,

title = {Design of Q-filter-based disturbance observer for differential algebraic equations and a robust stability condition: Zero relative degree case},

author = {Hamin Chang and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2023/11/Preprint-CT230915.pdf, Preprint},

doi = {10.1109/CDC49753.2023.10383698},

year  = {2023},

date = {2023-12-15},

urldate = {2023-12-15},

booktitle = {Proc. 62nd IEEE Conf. Decision Control},

pages = {8489-8494},

publisher = {IEEE},

abstract = {While the disturbance observer (DOB)-based controller is widely utilized in various practical applications, there has been a lack of extension of its use to differential algebraic equations (DAEs). In this paper, we introduce several lemmas that establish necessary and/or sufficient conditions for specifying the relative degree of DAEs. Using these lemmas, we also figure out that there is a class of DAEs which can be viewed as linear systems with zero relative degree. For the class of DAEs, we propose a design of Q-filter-based DOB as well as a robust stability condition for systems controlled by the DOB through time domain analysis using singular perturbation theory. The proposed stability condition is verified by an illustrative example.},

keywords = {DAEs, observer, relative-degree, stability},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{SutrTren23c,

title = {Inhomogeneous singular linear switched systems in discrete time: Solvability, reachability, and controllability Characterizations},

author = {Sutrisno and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2023/11/Preprint-ST230915.pdf, Preprint},

doi = {10.1109/CDC49753.2023.10384306},

year  = {2023},

date = {2023-12-14},

urldate = {2023-12-14},

booktitle = {Proc. 62nd IEEE Conf. Decision Control},

pages = {5869-5874},

publisher = {IEEE},

address = {Singapore},

abstract = {In this paper we study a novel solvability notion for discrete-time singular linear switched systems with inputs. We consider the existence and uniqueness of a solution on arbitrary finite time intervals with arbitrary inputs and arbitrary switching signals, and furthermore, we pay special attention to strict causality, i.e. the current state is only allowed to depend on past values of the state and the input. A necessary and sufficient condition for this solvability notion is then established. Furthermore, a surrogate switched system (an ordinary switched system that has equivalent input-output behavior) is derived for any solvable system. By utilizing those surrogate systems, we are able to characterize the reachability and controllability properties of the original singular systems using a geometric approach.},

keywords = {controllability, DAEs, discrete-time, solution-theory, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{SutrYin23,

title = {Nonlinear singular switched systems in discrete-time: solution theory and incremental stability under restricted switching signals},

author = {Sutrisno and Hao Yin and Stephan Trenn and Bayu Jayawardhana},

url = {https://stephantrenn.net/wp-content/uploads/2023/11/Preprint-SYTJ230914.pdf, Preprint},

doi = {10.1109/CDC49753.2023.10383278},

year  = {2023},

date = {2023-12-13},

urldate = {2023-09-14},

booktitle = {Proc. 62nd IEEE Conf. Decision Control},

pages = {914-919},

publisher = {IEEE},

address = {Singapore},

abstract = {In this article the solvability analysis of discrete-time nonlinear singular switched systems with restricted switching signals is studied. We provide necessary and sufficient conditions for the solvability analysis under fixed switching signals and fixed mode sequences. The so-called surrogate systems (ordinary systems that have the equivalent behavior to the original switched systems) are introduced for solvable switched systems. Incremental stability, which ensures that all solution trajectories converge with each other, is then studied by utilizing these surrogate systems. Sufficient (and necessary) conditions are provided for this stability analysis using single and switched Lyapunov function approaches.},

keywords = {DAEs, discrete-time, nonlinear, solution-theory, stability, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{ChenTren22b,

title = {Stability analysis of switched nonlinear differential-algebraic equations via nonlinear Weierstrass form},

author = {Yahao Chen and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2022/03/Preprint-CT220329.pdf, Preprint},

doi = {10.23919/ECC55457.2022.9838148},

year  = {2022},

date = {2022-07-12},

urldate = {2022-07-12},

booktitle = {Proceedings of the 2022 European Control Conference (ECC)},

pages = {1091-1096},

address = {London},

abstract = {In this paper, we propose some sufficient conditions for checking the asymptotic stability of switched nonlinear differential-algebraic equations (DAEs) under arbitrary switch- ing signal. We assume that each model of a given switched DAE is externally equivalent to a nonlinear Weierstrass form. With the help of this form, we can define nonlinear consistency projectors and jump-flow solutions for switched nonlinear DAEs. Then we use a different approach from the paper [12] to study the stability of switched DAEs via a novel notion called the jump-flow explicitation, which attaches a nonlinear control system to a given nonlinear DAE and can be used to simplify the common Lyapunov function conditions for both the flow and the jump dynamics of switched nonlinear DAEs. At last, a numerical example is given to illustrate how to check the stability of a switched nonlinear DAE by constructing a common Lyapunov function.

},

keywords = {DAEs, nonlinear, solution-theory, stability, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{MostTren22b,

title = {An averaged model for switched systems with state jumps applicable for PWM descriptor systems},

author = {Elisa Mostacciuolo and Stephan Trenn and Francesco Vasca},

url = {https://stephantrenn.net/wp-content/uploads/2022/03/Preprint-MTV220329.pdf, Preprint},

doi = {10.23919/ECC55457.2022.9838189},

year  = {2022},

date = {2022-07-12},

urldate = {2022-07-12},

booktitle = {Proceedings of the 2022 European Control Conference (ECC)},

pages = {1085-1090},

address = {London},

abstract = {Switched descriptor systems with pulse width modulation are characterized by modes whose dynamics are described by differential algebraic equations; this type of models can be viewed as switched impulsive systems, i.e. switched systems with ordinary differential equations as modes dynamics and state jumps at the switching time instants. The presence of possible jumps in the state makes the application of the classical averaging technique nontrivial. In this paper we propose an averaged model for switched impulsive systems. The state trajectory of the proposed averaged model is shown to approximate the one of the original system with an error of order of the switching period. The model reduces to the classical averaged model when there are no jumps in the state. The practical interest of the theoretical averaging result is demonstrated through numerical simulations of a switched capacitor electrical circuit.},

keywords = {averaging, DAEs, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{WijnTren21b,

title = {Optimal control of DAEs with unconstrained terminal costs},

author = {Paul Wijnbergen and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2021/09/Preprint-WT210927.pdf, Preprint},

doi = {10.1109/CDC45484.2021.9682950},

year  = {2021},

date = {2021-09-27},

urldate = {2021-09-27},

booktitle = {Proc. 60th IEEE Conf. Decision and Control (CDC 2021)},

pages = {5275-5280},

abstract = {This paper is concerned with the linear quadratic optimal control problem for impulse controllable differential algebraic equations on a bounded half open interval. Regarding the cost functional, a general positive semi-definite weight matrix is considered in the terminal cost. It is shown that for this problem, there generally does not exist an input that minimizes the cost functional. First it is shown that the problem can be reduced to finding an input to an index-1 DAE that minimizes a different quadratic cost functional. Second, necessary and sufficient conditions in terms of matrix equations are given for the existence of an optimal control.},

keywords = {DAEs, optimal-control, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{ChenTren21b,

title = {On geometric and differentiation index of nonlinear differential-algebraic equations},

author = {Yahao Chen and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2022/03/ChenTren21b.pdf, Paper},

doi = {10.1016/j.ifacol.2021.06.075},

year  = {2021},

date = {2021-04-06},

urldate = {2021-04-06},

booktitle = {IFAC-PapersOnLine (Proceedings of the MTNS 2020/21)},

volume = {54},

number = {9},

pages = {186-191},

publisher = {Elsevier},

organization = {IFAC},

abstract = {We discuss two notions of index, i.e., the geometric index and the differentiation index for nonlinear differential-algebraic equations (DAEs). First, we analyze solutions of nonlinear DAEs by revising a geometric reduction method (see e.g. Rabier and Rheinboldt (2002),Riaza (2008)). Then we show that although both of the geometric index and the differentiation index serve as a measure of difficulties for solving DAEs, they are actually related to the existence and uniqueness of solutions in a different manner. It is claimed in (Campbell and Gear, 1995) that the two indices coincide when sufficient smoothness and assumptions are satisfied, we elaborate this claim and show that the two indices indeed coincide if and only if a condition of uniqueness of solutions is satisfied (under certain constant rank assumptions). Finally, an example of a pendulum system is used to illustrate our results on the two indices.},

note = {open access},

keywords = {DAEs, nonlinear, solution-theory},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{ChenTren21c,

title = {An approximation for nonlinear differential-algebraic equations via singular perturbation theory},

author = {Yahao Chen and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2022/03/ChenTren21c.pdf, Paper

},

doi = {10.1016/j.ifacol.2021.08.496},

year  = {2021},

date = {2021-03-26},

urldate = {2021-03-26},

booktitle = {Proceedings of 7th IFAC Conference on Analysis and Design of Hybrid Systems (ADHS21), IFAC-PapersOnLine},

volume = {54},

number = {5},

pages = {187-192},

address = {Brussels, Belgium},

abstract = {In this paper, we study the jumps of nonlinear DAEs caused by inconsistent initial values. First, we propose a simple normal form called the index-1 nonlinear Weierstrass form (INWF) for nonlinear DAEs. Then we generalize the notion of consistency projector introduced in Liberzon and Trenn (2009) for linear DAEs to the nonlinear case. By an example, we compare our proposed nonlinear consistency projectors with two existing consistent initialization methods (one is from the paper Liberzon and Trenn (2012) and the other is given by a MATLAB function) to show that the two existing methods are not coordinate-free, i.e., the consistent points calculated by the two methods are not invariant under nonlinear coordinates transformations. Next we propose a singular perturbed system approximation for nonlinear DAEs, which is an ordinary differential equation (ODE) with a small perturbation parameter and we show that the solutions of the proposed perturbation system approximate both the jumps resulting from the nonlinear consistency projectors and the C1-solutions of the DAE. At last, we use a numerical simulation of a nonlinear DAE model arising from an electric circuit to illustrate the effectiveness of the proposed singular perturbed system approximation of DAEs.},

note = {open access},

keywords = {DAEs, nonlinear, normal-forms, solution-theory},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{TrenUnge20,

title = {Unimodular transformations for DAE initial trajectory problems},

author = {Stephan Trenn and Benjamin Unger},

url = {https://stephantrenn.net/wp-content/uploads/2021/01/pamm.202000322.pdf, Paper},

doi = {10.1002/pamm.202000322},

year  = {2021},

date = {2021-01-26},

booktitle = {PAMM · Proc. Appl. Math. Mech.},

volume = {20},

number = {1},

pages = {e202000322},

publisher = {Wiley-VCH GmbH},

abstract = {We consider linear time-invariant differential-algebraic equations (DAEs). For high-index DAEs, it is often the first step to perform an index reduction, which can be realized with a unimodular matrix. In this contribution, we illustrate the effect of unimodular transformations on initial trajectory problems associated with DAEs.},

note = {Open Access.},

keywords = {DAEs, piecewise-smooth-distributions, solution-theory},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{ChenTren21a,

title = {The differentiation index of nonlinear differential-algebraic equations versus the relative degree of nonlinear control systems},

author = {Yahao Chen and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2021/01/pamm.202000162.pdf, Paper},

doi = {10.1002/pamm.202000162},

year  = {2021},

date = {2021-01-25},

booktitle = {PAMM · Proc. Appl. Math. Mech. 2020},

volume = {20},

number = {1},

pages = {e202000162},

publisher = {Wiley-VCH GmbH},

abstract = {It is claimed in [1] that the notion of the relative degree in nonlinear control theory is closely related to that of the differen- tiation index for nonlinear differential-algebraic equations (DAEs). In this paper, we give more insights on this claim via a recent proposed concept (see [2]) called the explicitation of DAEs. The explicitation attaches a class of control systems to a given DAE, we show that the relative degree of the systems in the explicitation class is invariant in some sense and that the differentiation index of the original DAE coincides with the maximum of the relative degree of the explicitation systems.},

note = {Open Access.},

keywords = {DAEs, nonlinear, normal-forms, relative-degree},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{WijnJeen20,

title = {On stabilizability of switched differential algebraic equations},

author = {Paul Wijnbergen and Mark Jeeninga and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2021/06/WijnJeen20.pdf, Paper},

doi = {10.1016/j.ifacol.2020.12.2580},

year  = {2020},

date = {2020-07-06},

booktitle = {IFAC-PapersOnLine 53-2},

pages = {4304-4309},

abstract = {This paper considers stabilizability of switched differential algebraic equations (DAEs). We first introduce the notion of interval stabilizability and show that under a certain uniformity assumption, stabilizability can be concluded from interval stabilizability. A geometric approach is taken to find necessary and sufficient conditions for interval stabilizability. This geometric approach can also be utilized to derive a novel characterization of controllability.},

note = {Proc. IFAC World Congress 2020, Berlin, Germany. Open access.},

keywords = {DAEs, stability, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{WijnTren20,

title = {Impulse controllability of switched differential-algebraic equations},

author = {Paul Wijnbergen and Stephan Trenn},

url = {https://stephantrenn.net/wp-content/uploads/2020/02/Preprint-WT200204.pdf, Preprint},

doi = {10.23919/ECC51009.2020.9143713},

year  = {2020},

date = {2020-05-15},

booktitle = {Proc. European Control Conference (ECC 2020)},

pages = {1561-1566},

address = {Saint Petersburg, Russia},

abstract = {This paper addresses impulse controllability of switched DAEs on a finite interval. First we present a forward approach where we define certain subspaces forward in time. These subpsaces are then used to provide a sufficient condition for impulse controllability. In order to obtain a full characterization we present afterwards a backward approach, where a sequence of subspaces is defined backwards in time. With the help of the last element of this backward sequence, we are able to fully characterize impulse controllability. All results are geometric results and thus independent of a coordinate system.},

keywords = {controllability, DAEs, piecewise-smooth-distributions, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{TrenUnge19,

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},

doi = {10.1109/CDC40024.2019.9030146},

year  = {2019},

date = {2019-12-12},

booktitle = {Proc. 58th IEEE Conf. Decision Control (CDC) 2019},

pages = {989-994},

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.},

keywords = {DAEs, delay, solution-theory},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{KausTren18,

title = {Water hammer modeling for water networks via hyperbolic PDEs and switched DAEs},

author = {Rukhsana Kausar and Stephan Trenn},

editor = {Christian Klingenberg and Michael Westdickenberg},

url = {https://stephantrenn.net/wp-content/uploads/2017/09/Preprint-KT170418.pdf, Preprint},

doi = {10.1007/978-3-319-91548-7_9},

isbn = {978-3-319-91548-7},

year  = {2018},

date = {2018-06-27},

urldate = {2018-06-27},

booktitle = {Theory, Numerics and Applications of Hyperbolic Problems II},

pages = {123-135},

publisher = {Springer},

address = {Cham},

abstract = {In water distribution network instantaneous changes in valve and pump settings introduce jumps and sometimes impulses. In particular, a particular impulsive phenomenon which occurs due to sudden closing of valve is the so called water hammer. It is classically modeled as a system of hyperbolic partial differential equations (PDEs). We observed that under some suitable assumptions the PDEs usually used to describe water flows can be simplified to differential algebraic equations (DAEs). The idea is to model water hammer phenomenon in the switched DAEs framework due to its special feature of studying such impulsive effects. To compare these two modeling techniques, a system of hyperbolic PDE model and the switched DAE model for a simple set up consisting of two reservoirs, six pipes and three valve is presented. The aim of this contribution is to present results of both models as motivation for the claim that a switched DAE modeling framework is suitable for describing a water hammer.},

note = {Presented at XVI International Conference on Hyperbolic Problems (HYP2016), Aachen},

keywords = {application, DAEs, nonlinear, PDEs, piecewise-smooth-distributions, solution-theory, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@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, DAEs, nonlinear, piecewise-smooth-distributions, solution-theory, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@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 = {DAEs, observability, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{KustPati17a,

title = {Indiscernible topological variations in DAE networks with applications to power grids},

author = {Ferdinand Küsters and Deepak Patil and Pietro Tesi and Stephan Trenn},

url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-KPTT170320.pdf, Preprint},

doi = {10.1016/j.ifacol.2017.08.1478},

issn = {2405-8963},

year  = {2017},

date = {2017-03-24},

booktitle = {Proc. 20th IFAC World Congress 2017},

journal = {IFAC-PapersOnLine},

volume = {50},

number = {1},

pages = {7333 - 7338},

address = {Toulouse, France},

abstract = {The ability to detect topology variations in dynamical networks defined by differential algebraic equations (DAEs) is considered. We characterize the existence of initial states, for which topological changes are indiscernible. A key feature of our characterization is the ability to verify indiscernibility just in terms of the nominal topology. We apply the results to a power grid model and also discuss the relationship to recent mode-detection results for switched DAEs.},

keywords = {application, DAEs, networks, observability},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{KallKaus17,

title = {Modeling water hammers via PDEs and switched DAEs with numerical justification},

author = {Jochen Kall and Rukhsana Kausar and Stephan Trenn},

url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-KKT170324.pdf, Preprint},

doi = {10.1016/j.ifacol.2017.08.927},

issn = {2405-8963},

year  = {2017},

date = {2017-03-23},

booktitle = {Proc. 20th IFAC World Congress 2017},

journal = {IFAC-PapersOnLine},

volume = {50},

number = {1},

pages = {5349 - 5354},

address = {Toulouse, France},

abstract = {In water distribution networks instantaneous changes in valve and pump settings may introduces jumps and peaks in the pressure. In particular, a well known phenomenon in response to the sudden closing of a valve is the so called water hammer, which (if not taken into account properly) may destroy parts of the water network. It is classically modeled as a system of hyperbolic partial differential equations (PDEs). After discussing this PDE model we propose a simplified model using switched differential-algebraic equations (DAEs). Switched DAEs are known to be able to produce infinite peaks in response to sudden structural changes. These peaks (in the mathematical form of Dirac impulses) can easily be predicted and may allow for a simpler analysis of complex water networks in the future. As a first step toward that goal, we verify the novel modeling approach by comparing these two modeling techniques numerically for a simple set up consisting of two reservoirs, a pipe and a valve.},

keywords = {application, DAEs, nonlinear, PDEs, solution-theory, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{TanwTren17b,

title = {Observer design for detectable switched  differential-algebraic equations},

author = {Aneel Tanwani and Stephan Trenn},

url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-TT170320.pdf, Preprint},

doi = {10.1016/j.ifacol.2017.08.659},

issn = {2405-8963},

year  = {2017},

date = {2017-03-22},

booktitle = {Proc. 20th IFAC World Congress 2017},

journal = {IFAC-PapersOnLine},

volume = {50},

number = {1},

pages = {2953 - 2958},

address = {Toulouse, France},

abstract = {This paper studies detectability for switched linear differential-algebraic equations (DAEs) and its application in synthesis of observers. Equating detectability to asymptotic stability of zero-output-constrained state trajectories, and building on our work on interval-wise observability, we propose the notion of interval-wise detectability: If the output of the system is constrained to be identically zero over an interval, then the norm of the corresponding state trajectories scales down by a certain factor over that interval. Conditions are provided under which the interval-wise detectability leads to asymptotic stability of zero-output-constrained state trajectories. An application is demonstrated in designing state estimators. Decomposing the state into observable and unobservable components, we show that if the observable component in the estimator is reset appropriately and persistently, then the estimation error converges to zero asymptotically under the interval-wise detectability assumption.},

keywords = {DAEs, observability, observer, piecewise-smooth-distributions, stability, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@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 = {DAEs, nonlinear, solution-theory},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{Tren16,

title = {Stabilization of switched DAEs via fast switching},

author = {Stephan Trenn},

url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-Tre160511.pdf, Preprint},

doi = {10.1002/pamm.201610402},

issn = {1617-7061},

year  = {2016},

date = {2016-05-12},

booktitle = {PAMM - Proc. Appl. Math. Mech.},

volume = {16},

number = {1},

pages = {827--828},

publisher = {WILEY-VCH Verlag},

abstract = {Switched differential algebraic equations (switched DAEs) can model dynamical systems with state constraints together with sudden structural changes (switches). These switches may lead to induced jumps and can destabilize the system even in the case that each mode is stable. However, the opposite effect is also possible; in particular, the question of finding a stabilizing switching signal is of interest. Two approaches are presented how to stabilize a switched DAE via fast switching.},

keywords = {averaging, DAEs, stability, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{KustTren16b,

title = {Observer design based on constant-input observability for DAEs},

author = {Ferdinand Küsters and Stephan Trenn and Andreas Wirsen},

url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-KTW160511.pdf, Preprint},

doi = {10.1002/pamm.201610395},

issn = {1617-7061},

year  = {2016},

date = {2016-01-01},

booktitle = {PAMM - Proc. Appl. Math. Mech.},

volume = {16},

number = {1},

pages = {813--814},

publisher = {WILEY-VCH Verlag},

abstract = {For differential-algebraic equations (DAEs) an observability notion is considered which assumes the input to be unknown and constant. Based on this, an observer design is proposed.},

keywords = {DAEs, observability, observer},

pubstate = {published},

tppubtype = {inproceedings}

}

@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, DAEs, piecewise-smooth-distributions, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@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 = {DAEs, observability, stability, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@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, DAEs, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{KustTren15a,

title = {Controllability characterization of switched DAEs},

author = {Ferdinand Küsters and Stephan Trenn},

url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-KT150527.pdf, Preprint},

doi = {10.1002/pamm.201510311},

issn = {1617-7061},

year  = {2015},

date = {2015-06-01},

booktitle = {PAMM - Proc. Appl. Math. Mech.},

volume = {15},

number = {1},

pages = {643--644},

publisher = {WILEY-VCH Verlag},

abstract = {We study controllability of switched differential algebraic equations (switched DAEs) with fixed switching signal. Based on a behavioral definition of controllability we are able to establish a controllability characterization that takes into account possible jumps and impulses induced by the switches.},

keywords = {controllability, DAEs, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{MostTren15a,

title = {Partial averaging for switched DAEs with two modes},

author = {Elisa Mostacciuolo and Stephan Trenn and Francesco Vasca},

url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-MTV150316.pdf, Preprint},

doi = {10.1109/ECC.2015.7330977},

year  = {2015},

date = {2015-03-01},

booktitle = {Proc. 2015 European Control Conf. (ECC), Linz, Austria},

pages = {2896--2901},

abstract = {In this paper an averaging result for switched systems whose modes are represented by means of differential algebraic equations (DAEs) is presented. Homogeneous switched DAEs with periodic switchings between two modes are considered. It is proved that a (switched) averaged system can be defined also in the presence of state jumps whose amplitude does not decrease with the increasing of the switching frequency. A switched capacitor electrical circuit is considered as an illustrative example.},

keywords = {averaging, DAEs, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{GrosTren14,

title = {Topological solvability and index characterizations for a common DAE power system model},

author = {Tjorben B. Gross and Stephan Trenn and Andreas Wirsen},

url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-GTW140904.pdf, Preprint},

doi = {10.1109/CCA.2014.6981321},

year  = {2014},

date = {2014-10-10},

booktitle = {Proc. 2014 IEEE Conf. Control Applications (CCA)},

pages = {9--14},

organization = {IEEE},

abstract = {For the widely-used power system model consisting of the generator swing equations and the power flow equations resulting in a system of differential algebraic equations (DAEs), we introduce a sufficient and necessary solvability condition for the linearized model. This condition is based on the topological structure of the power system. Furthermore we show sufficient conditions for the linearized DAE-system and a nonlinear version of the model to have differentiation index equal to one.},

keywords = {application, DAEs, networks, nonlinear, solution-theory},

pubstate = {published},

tppubtype = {inproceedings}

}

@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 = {DAEs, observability, observer, piecewise-smooth-distributions, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@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 = {DAEs, solution-theory, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@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, DAEs, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{IannPedi13c,

title = {Averaging for switched DAEs},

author = {Luigi Iannelli and Carmen Pedicini and Stephan Trenn and Francesco Vasca},

url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-IPTV130527.pdf, Preprint},

doi = {10.1002/pamm.201310237},

issn = {1617-7061},

year  = {2013},

date = {2013-10-01},

booktitle = {PAMM - Proc. Appl. Math. Mech.},

volume = {13},

number = {1},

pages = {489--490},

publisher = {WILEY-VCH Verlag},

abstract = {Switched differential-algebraic equations (switched DAEs) E_sigma(t) x'(t) = A_sigma(t) x(t) are suitable for modeling many practical systems, e.g. electrical circuits. When the switching is periodic and of high frequency, the question arises whether the solutions of switched DAEs can be approximated by an average non-switching system. It is well known that for a quite general class of switched ordinary differential equations (ODEs) this is the case. For switched DAEs, due the presence of the so-called consistency projectors, it is possible that the limit of trajectories for faster and faster switching does not exist. Under certain assumptions on the consistency projectors a result concerning the averaging for switched DAEs is presented.},

keywords = {averaging, DAEs, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{IannPedi13a,

title = {On averaging for switched linear differential algebraic equations},

author = {Luigi Iannelli and Carmen Pedicini and Stephan Trenn and Francesco Vasca},

url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-IPTV130326.pdf, Preprint

http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6669240, IEEE Xplore Article Number 6669240},

year  = {2013},

date = {2013-07-02},

booktitle = {Proc. 12th European Control Conf. (ECC) 2013, Zurich, Switzerland},

pages = {2163 -- 2168},

abstract = {Averaging is an effective technique which allows the analysis and control design of nonsmooth switched systems through the use of corresponding simpler smooth averaged systems. Approximation results and stability analysis have been presented in the literature for dynamic systems described by switched ordinary differential equations. In this paper the averaging technique is shown to be useful also for the analysis of switched systems whose modes are represented by means of differential algebraic equations (DAEs). An approximation result is derived for a simple but representative homogenous switched DAE with periodic switching signals and two modes. Simulations based on a simple electric circuit model illustrate the theoretical result.},

keywords = {averaging, DAEs, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@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 = {DAEs, piecewise-smooth-distributions, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@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 = {DAEs, Lyapunov, stability, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@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 = {DAEs, observability, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{TrenWirt12a,

title = {A converse Lyapunov theorem for switched DAEs},

author = {Stephan Trenn and Fabian Wirth},

url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-TW120508.pdf, Preprint},

doi = {10.1002/pamm.201210381},

issn = {1617-7061},

year  = {2012},

date = {2012-03-02},

booktitle = {PAMM - Proc. Appl. Math. Mech.},

volume = {12},

number = {1},

pages = {789--792},

publisher = {WILEY-VCH Verlag},

abstract = {For switched ordinary differential equations (ODEs) it is well known that exponential stability under arbitrary switching yields the existence of a common Lyapunov function. The result is known as a “converse Lyapunov Theorem”. In this note we will present a converse Lyapunov theorem for switched differential algebraic equations (DAEs) as well as the construction of a Barabanov norm for irreducible switched DAEs.},

keywords = {DAEs, Lyapunov, stability, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@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 = {DAEs, Lyapunov, stability, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@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, DAEs, piecewise-smooth-distributions, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@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 = {DAEs, observability, piecewise-smooth-distributions, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@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 = {DAEs, Lyapunov, stability, switched-DAEs, switched-systems},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{Tren08b,

title = {Distributional solution theory for linear DAEs},

author = {Stephan Trenn},

url = {http://stephantrenn.net/wp-content/uploads/2017/09/Preprint-Tre080424.pdf, Preprint},

doi = {10.1002/pamm.200810077},

issn = {1617--7061},

year  = {2008},

date = {2008-05-01},

booktitle = {PAMM - Proc. Appl. Math. Mech.},

volume = {8},

number = {1},

pages = {10077--10080},

publisher = {WILEY-VCH Verlag},

abstract = {A solution theory for switched linear differential–algebraic equations (DAEs) is developed. To allow for non–smooth coordinate transformation, the coefficients matrices may have distributional entries. Since also distributional solutions are considered it is necessary to define a suitable multiplication for distribution. This is achieved by restricting the space of distributions to the smaller space of piecewise–smooth distributions. Solution formulae for two special DAEs, distributional ordinary differential equations (ODEs) and pure distributional DAEs, are given.},

keywords = {DAEs, piecewise-smooth-distributions, solution-theory},

pubstate = {published},

tppubtype = {inproceedings}

}