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-, conference-, and submitted publications.

## 2021 |

Chen, Yahao; Trenn, Stephan; Respondek, Witold Normal forms and internal regularization of nonlinear differential-algebraic control systems Journal Article International Journal of Robust and Nonlinear Control, 2021 , pp. 1-22, 2021, (Open access). Abstract | Links | BibTeX | Tags: DAEs, nonlinear, normal-forms, open-access, solution-theory @article{ChenTren21d, title = {Normal forms and internal regularization of nonlinear differential-algebraic control systems}, author = {Yahao Chen and Stephan Trenn and Witold Respondek}, url = {https://stephantrenn.net/wp-content/uploads/2021/06/ChenTren21d.pdf, Paper}, doi = {10.1002/rnc.5623}, year = {2021}, date = {2021-04-13}, journal = {International Journal of Robust and Nonlinear Control}, volume = {2021}, pages = {1-22}, abstract = {In this paper, we propose two normal forms for nonlinear differential-algebraic control systems (DACSs) under external feedback equivalence, using a notion called maximal controlled invariant submanifold. The two normal forms simplify the system structures and facilitate understanding the various roles of variables for nonlinear DACSs. Moreover, we study when a given nonlinear DACS is internally regularizable, i.e., when there exists a state feedback transforming the DACS into a differential-algebraic equation (DAE) with internal regularity, the latter notion is closely related to the existence and uniqueness of solutions of DAEs. We also revise a commonly used method in DAE solution theory, called the geometric reduction method. We apply this method to DACSs and formulate it as an algorithm, which is used to construct maximal controlled invariant submanifolds and to find internal regularization feedbacks. Two examples of mechanical systems are used to illustrate the proposed normal forms and to show how to internally regularize DACSs.}, note = {Open access}, keywords = {DAEs, nonlinear, normal-forms, open-access, solution-theory}, pubstate = {published}, tppubtype = {article} } In this paper, we propose two normal forms for nonlinear differential-algebraic control systems (DACSs) under external feedback equivalence, using a notion called maximal controlled invariant submanifold. The two normal forms simplify the system structures and facilitate understanding the various roles of variables for nonlinear DACSs. Moreover, we study when a given nonlinear DACS is internally regularizable, i.e., when there exists a state feedback transforming the DACS into a differential-algebraic equation (DAE) with internal regularity, the latter notion is closely related to the existence and uniqueness of solutions of DAEs. We also revise a commonly used method in DAE solution theory, called the geometric reduction method. We apply this method to DACSs and formulate it as an algorithm, which is used to construct maximal controlled invariant submanifolds and to find internal regularization feedbacks. Two examples of mechanical systems are used to illustrate the proposed normal forms and to show how to internally regularize DACSs. |

Iervolino, Raffaele; Trenn, Stephan; Vasca, Francesco Asymptotic stability of piecewise affine systems with Filippov solutions via discontinuous piecewise Lyapunov functions Journal Article IEEE Transactions on Automatic Control, 66 (4), pp. 1513-1528, 2021. Abstract | Links | BibTeX | Tags: nonlinear, open-access, solution-theory, stability, switched-systems @article{IervTren21, title = {Asymptotic stability of piecewise affine systems with Filippov solutions via discontinuous piecewise Lyapunov functions}, author = {Raffaele Iervolino and Stephan Trenn and Francesco Vasca}, url = {https://stephantrenn.net/wp-content/uploads/2020/02/Preprint-ITV200204.pdf, Preprint}, doi = {10.1109/TAC.2020.2996597}, year = {2021}, date = {2021-04-01}, journal = {IEEE Transactions on Automatic Control}, volume = {66}, number = {4}, pages = {1513-1528}, abstract = {Asymptotic stability of continuous-time piecewise affine systems defined over a polyhedral partition of the state space, with possible discontinuous vector field on the boundaries, is considered. In the first part of the paper the feasible Filippov solution concept is introduced by characterizing single-mode Caratheodory, sliding mode and forward Zeno behaviors. Then, a global asymptotic stability result through a (possibly discontinuous) piecewise Lyapunov function is presented. The sufficient conditions are based on pointwise classifications of the trajectories which allow the identification of crossing, unreachable and Caratheodory boundaries. It is shown that the sign and jump conditions of the stability theorem can be expressed in terms of linear matrix inequalities by particularizing to piecewise quadratic Lyapunov functions and using the cone-copositivity approach. Several examples illustrate the theoretical arguments and the effectiveness of the stability result.}, keywords = {nonlinear, open-access, solution-theory, stability, switched-systems}, pubstate = {published}, tppubtype = {article} } Asymptotic stability of continuous-time piecewise affine systems defined over a polyhedral partition of the state space, with possible discontinuous vector field on the boundaries, is considered. In the first part of the paper the feasible Filippov solution concept is introduced by characterizing single-mode Caratheodory, sliding mode and forward Zeno behaviors. Then, a global asymptotic stability result through a (possibly discontinuous) piecewise Lyapunov function is presented. The sufficient conditions are based on pointwise classifications of the trajectories which allow the identification of crossing, unreachable and Caratheodory boundaries. It is shown that the sign and jump conditions of the stability theorem can be expressed in terms of linear matrix inequalities by particularizing to piecewise quadratic Lyapunov functions and using the cone-copositivity approach. Several examples illustrate the theoretical arguments and the effectiveness of the stability result. |

## 2020 |

Borsche, Raul; Kocoglu, Damla; Trenn, Stephan A distributional solution framework for linear hyperbolic PDEs coupled to switched DAEs Journal Article Mathematics of Control, Signals, and Systems (MCSS), 32 , pp. 455-487, 2020, (Open Access). Abstract | Links | BibTeX | Tags: DAEs, delay, networks, open-access, PDEs, piecewise-smooth-distributions, solution-theory, switched-DAEs @article{BorsKoco20, title = {A distributional solution framework for linear hyperbolic PDEs coupled to switched DAEs}, author = {Raul Borsche and Damla Kocoglu and Stephan Trenn}, url = {https://stephantrenn.net/wp-content/uploads/2020/11/23-MCSS2020.pdf, Paper}, doi = {10.1007/s00498-020-00267-7}, year = {2020}, date = {2020-11-18}, journal = {Mathematics of Control, Signals, and Systems (MCSS)}, volume = {32}, pages = {455-487}, abstract = {A distributional solution framework is developed for systems con- sisting of linear hyperbolic partial differential equations (PDEs) and switched differential-algebraic equations (DAEs) which are coupled via boundary conditions. The unique solvability is then characterize in terms of a switched delay DAE. The theory is illustrated with an example of electric power lines modeled by the telegraph equations which are coupled via a switching transformer where simulations confirm the predicted impulsive solutions.}, note = {Open Access}, keywords = {DAEs, delay, networks, open-access, PDEs, piecewise-smooth-distributions, solution-theory, switched-DAEs}, pubstate = {published}, tppubtype = {article} } A distributional solution framework is developed for systems con- sisting of linear hyperbolic partial differential equations (PDEs) and switched differential-algebraic equations (DAEs) which are coupled via boundary conditions. The unique solvability is then characterize in terms of a switched delay DAE. The theory is illustrated with an example of electric power lines modeled by the telegraph equations which are coupled via a switching transformer where simulations confirm the predicted impulsive solutions. |

Wijnbergen, Paul; Jeeninga, Mark; Trenn, Stephan On stabilizability of switched differential algebraic equations Inproceedings IFAC-PapersOnLine 53-2, pp. 4304-4309, 2020, (Proc. IFAC World Congress 2020, Berlin, Germany. Open access.). Abstract | Links | BibTeX | Tags: DAEs, open-access, stability, switched-DAEs, switched-systems @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, open-access, stability, switched-DAEs, switched-systems}, pubstate = {published}, tppubtype = {inproceedings} } 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. |

Hossain, Sumon; Trenn, Stephan A time-varying Gramian based model reduction approach for Linear Switched Systems Inproceedings IFAC PapersOnline 53-2, pp. 5629-5634, 2020, (Proc. IFAC World Congress 2020, Berlin, Germany. Open access.). Abstract | Links | BibTeX | Tags: model reduction, open-access, switched-systems @inproceedings{HossTren20a, title = {A time-varying Gramian based model reduction approach for Linear Switched Systems}, author = {Sumon Hossain and Stephan Trenn}, url = {https://stephantrenn.net/wp-content/uploads/2021/06/HossTren20a.pdf, Paper (open access)}, doi = {10.1016/j.ifacol.2020.12.1580}, year = {2020}, date = {2020-07-05}, booktitle = {IFAC PapersOnline 53-2}, pages = {5629-5634}, abstract = {We propose a model reduction approach for switched linear system based on a balanced truncation reduction method for linear time-varying systems. The key idea is to approximate the piecewise-constant coefficient matrices with continuous time-varying coefficients and then apply available balance truncation methods for (continuous) time-varying systems. The proposed method is illustrated with a low dimensional academic example.}, note = {Proc. IFAC World Congress 2020, Berlin, Germany. Open access.}, keywords = {model reduction, open-access, switched-systems}, pubstate = {published}, tppubtype = {inproceedings} } We propose a model reduction approach for switched linear system based on a balanced truncation reduction method for linear time-varying systems. The key idea is to approximate the piecewise-constant coefficient matrices with continuous time-varying coefficients and then apply available balance truncation methods for (continuous) time-varying systems. The proposed method is illustrated with a low dimensional academic example. |