2024
|
Mostacciuolo, Elisa; Trenn, Stephan; Vasca, Francesco Averaging for switched impulsive systems with pulse width modulation Journal Article In: Automatica, vol. 160, no. 111447, pp. 1-12, 2024, (open access). @article{MostTren24,
title = {Averaging for switched impulsive systems with pulse width modulation},
author = {Elisa Mostacciuolo and Stephan Trenn and Francesco Vasca},
url = {https://stephantrenn.net/wp-content/uploads/2024/02/MostTren24.pdf, Paper},
doi = {10.1016/j.automatica.2023.111447},
year = {2024},
date = {2024-02-01},
urldate = {2024-02-01},
journal = {Automatica},
volume = {160},
number = {111447},
pages = {1-12},
abstract = {Linear switched impulsive systems (SIS) are characterized by ordinary differential equations as modes dynamics and state jumps at the switching time instants. The presence of possible jumps in the state makes nontrivial the application of classical averaging techniques. In this paper we consider SIS with pulse width modulation (PWM) and we propose an averaged model whose solution approximates the moving average of the SIS solution with an error which decreases with the multiple of the switching period and by decreasing the PWM period. The averaging result requires milder assumptions on the system matrices with respect to those needed by the previous averaging techniques for SIS. The interest of the proposed model is strengthened by the fact that it reduces to the classical averaged model for PWM systems when there are no jumps in the state. The theoretical results are verified through numerical results obtained by considering a switched capacitor electrical circuit.},
note = {open access},
keywords = {application, averaging, DAEs, LMIs, switched-DAEs, switched-systems},
pubstate = {published},
tppubtype = {article}
}
Linear switched impulsive systems (SIS) are characterized by ordinary differential equations as modes dynamics and state jumps at the switching time instants. The presence of possible jumps in the state makes nontrivial the application of classical averaging techniques. In this paper we consider SIS with pulse width modulation (PWM) and we propose an averaged model whose solution approximates the moving average of the SIS solution with an error which decreases with the multiple of the switching period and by decreasing the PWM period. The averaging result requires milder assumptions on the system matrices with respect to those needed by the previous averaging techniques for SIS. The interest of the proposed model is strengthened by the fact that it reduces to the classical averaged model for PWM systems when there are no jumps in the state. The theoretical results are verified through numerical results obtained by considering a switched capacitor electrical circuit. |
2023
|
Yin, Hao; Jayawardhana, Bayu; Trenn, Stephan Stability of switched systems with multiple equilibria: a mixed stable-unstable subsystem case Journal Article In: Systems & Control Letters, vol. 180, no. 105622, pp. 1-9, 2023, (open access). @article{YinJaya23b,
title = {Stability of switched systems with multiple equilibria: a mixed stable-unstable subsystem case},
author = {Hao Yin and Bayu Jayawardhana and Stephan Trenn},
url = {https://stephantrenn.net/wp-content/uploads/2024/02/YinJaya23b.pdf, Paper},
doi = {10.1016/j.sysconle.2023.105622},
year = {2023},
date = {2023-10-01},
urldate = {2023-10-01},
journal = {Systems & Control Letters},
volume = {180},
number = {105622},
pages = {1-9},
abstract = {This paper studies the stability of switched systems that are composed of a mixture of stable and unstable modes with multiple equilibria. The main results of this paper include some sufficient conditions concerning set convergence of switched nonlinear systems. We show that under suitable dwell-time and leave-time switching laws, trajectories converge to an initial set and then stay in a convergent set. Based on these conditions, Linear Matrix Inequality (LMI) conditions are derived that allow for numerical validation of the practical stability of switched affine systems, which include those with all unstable modes. Two examples are provided to verify the theoretical results.},
note = {open access},
keywords = {LMIs, Lyapunov, stability, switched-systems},
pubstate = {published},
tppubtype = {article}
}
This paper studies the stability of switched systems that are composed of a mixture of stable and unstable modes with multiple equilibria. The main results of this paper include some sufficient conditions concerning set convergence of switched nonlinear systems. We show that under suitable dwell-time and leave-time switching laws, trajectories converge to an initial set and then stay in a convergent set. Based on these conditions, Linear Matrix Inequality (LMI) conditions are derived that allow for numerical validation of the practical stability of switched affine systems, which include those with all unstable modes. Two examples are provided to verify the theoretical results. |
Yin, Hao; Jayawardhana, Bayu; Trenn, Stephan On contraction analysis of switched systems with mixed contracting-noncontracting modes via mode-dependent average dwell time Journal Article In: IEEE Transactions on Automatic Control, vol. 68, iss. 10, pp. 6409-6416, 2023. @article{YinJaya23a,
title = {On contraction analysis of switched systems with mixed contracting-noncontracting modes via mode-dependent average dwell time},
author = {Hao Yin and Bayu Jayawardhana and Stephan Trenn},
url = {https://stephantrenn.net/wp-content/uploads/2022/04/Preprint-YJT221110.pdf, Preprint},
doi = {10.1109/TAC.2023.3237492},
year = {2023},
date = {2023-10-01},
urldate = {2023-01-16},
journal = {IEEE Transactions on Automatic Control},
volume = {68},
issue = {10},
pages = {6409-6416},
abstract = {This paper studies contraction analysis of switched systems that are composed of a mixture of contracting and non- contracting modes. The first result pertains to the equivalence of the contraction of a switched system and the uniform global ex- ponential stability of its variational system. Based on this equiva- lence property, sufficient conditions for a mode-dependent average dwell/leave-time based switching law to be contractive are estab- lished. Correspondingly, LMI conditions are derived that allow for numerical validation of contraction property of nonlinear switched systems, which include those with all non-contracting modes.},
keywords = {LMIs, Lyapunov, nonlinear, stability, switched-systems},
pubstate = {published},
tppubtype = {article}
}
This paper studies contraction analysis of switched systems that are composed of a mixture of contracting and non- contracting modes. The first result pertains to the equivalence of the contraction of a switched system and the uniform global ex- ponential stability of its variational system. Based on this equiva- lence property, sufficient conditions for a mode-dependent average dwell/leave-time based switching law to be contractive are estab- lished. Correspondingly, LMI conditions are derived that allow for numerical validation of contraction property of nonlinear switched systems, which include those with all non-contracting modes. |
2022
|
Yin, Hao; Jayawardhana, Bayu; Trenn, Stephan On contraction analysis of switched systems with mixed contracting-noncontracting modes via mode-dependent average dwell time Miscellaneous Book of Abstracts - 41th Benelux Meeting on Systems and Control, 2022. @misc{YinJaya22m,
title = {On contraction analysis of switched systems with mixed contracting-noncontracting modes via mode-dependent average dwell time},
author = {Hao Yin and Bayu Jayawardhana and Stephan Trenn},
editor = {Alain Vande Wouwer and Michel Kinnaert and Emanuele Garone and Laurent Dewasme and Guilherme A. Pimentel},
url = {https://stephantrenn.net/wp-content/uploads/2022/08/YinJaya22.pdf, Abstract
https://www.beneluxmeeting.nl/2022/uploads/images/2022/boa_BeneluxMeeting2022_Web_betaV12_withChairs.pdf, Book of Abstracts},
year = {2022},
date = {2022-07-07},
urldate = {2022-07-07},
howpublished = {Book of Abstracts - 41th Benelux Meeting on Systems and Control},
keywords = {LMIs, Lyapunov, stability, switched-systems, synchronization},
pubstate = {published},
tppubtype = {misc}
}
|
2021
|
Iervolino, Raffaele; Trenn, Stephan; Vasca, Francesco Asymptotic stability of piecewise affine systems with Filippov solutions via discontinuous piecewise Lyapunov functions Journal Article In: IEEE Transactions on Automatic Control, vol. 66, no. 4, pp. 1513-1528, 2021. @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},
urldate = {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 = {LMIs, Lyapunov, nonlinear, 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
|
Iervolino, Raffaele; Vasca, Francesco; Trenn, Stephan Discontinuous Lyapunov functions for discontinous piecewise-affine systems Miscellaneous Extended Abstract, 2020, (accepted for cancelled MTNS 20/21). @misc{IervTren20m,
title = {Discontinuous Lyapunov functions for discontinous piecewise-affine systems},
author = {Raffaele Iervolino and Francesco Vasca and Stephan Trenn},
url = {https://stephantrenn.net/wp-content/uploads/2020/01/Preprint-ITV200122.pdf, Extended Abstract},
year = {2020},
date = {2020-01-22},
urldate = {2020-01-22},
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. We first introduce the feasible Filippov solution concept 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 highlighted 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. },
howpublished = {Extended Abstract},
note = {accepted for cancelled MTNS 20/21},
keywords = {LMIs, Lyapunov, stability, switched-systems},
pubstate = {published},
tppubtype = {misc}
}
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. We first introduce the feasible Filippov solution concept 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 highlighted 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. |
2017
|
Iervolino, Raffaele; Trenn, Stephan; Vasca, Francesco Stability of piecewise affine systems through discontinuous piecewise quadratic Lyapunov functions Proceedings Article In: Proc. 56th IEEE Conf. Decis. Control, pp. 5894 - 5899, Melbourne, Australia, 2017. @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},
urldate = {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 piecewise 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 = {LMIs, 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 piecewise 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. |