Stability and convergence for systems with switching equilibria

Silvia Mastellone; Dušan M. Stipanović; Mark W. Spong

doi:10.1109/CDC.2007.4434822

Stability and convergence for systems with switching equilibria

Silvia Mastellone, Dušan M. Stipanović, Mark W. Spong

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

We study systems in which the equilibrium point varies discontinuously according to a well defined state or time-dependent switching law. We refer to those systems as systems with switching equilibria. To motivate our study, we describe a class of problems in engineering and biology that can be formulated using such systems. We study stability and convergence properties of those systems under various switching rules. In particular we prove convergence under arbitrary switching, time-dependent and state-dependent switching laws. In the time-dependent switching case we highlight connections between the relaxation theorem corresponding to differential inclusions, Pulse-Width-Modulation (PWM) and averaging theory.

Original language	English (US)
Title of host publication	Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	4013-4020
Number of pages	8
ISBN (Print)	1424414989, 9781424414987
DOIs	https://doi.org/10.1109/CDC.2007.4434822
State	Published - 2007
Event	46th IEEE Conference on Decision and Control 2007, CDC - New Orleans, LA, United States Duration: Dec 12 2007 → Dec 14 2007

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Other

Other	46th IEEE Conference on Decision and Control 2007, CDC
Country/Territory	United States
City	New Orleans, LA
Period	12/12/07 → 12/14/07

ASJC Scopus subject areas

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

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10.1109/CDC.2007.4434822

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Mastellone, S., Stipanović, D. M., & Spong, M. W. (2007). Stability and convergence for systems with switching equilibria. In Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC (pp. 4013-4020). Article 4434822 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2007.4434822

Stability and convergence for systems with switching equilibria. / Mastellone, Silvia; Stipanović, Dušan M.; Spong, Mark W.
Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC. Institute of Electrical and Electronics Engineers Inc., 2007. p. 4013-4020 4434822 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Mastellone, S, Stipanović, DM & Spong, MW 2007, Stability and convergence for systems with switching equilibria. in Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC., 4434822, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 4013-4020, 46th IEEE Conference on Decision and Control 2007, CDC, New Orleans, LA, United States, 12/12/07. https://doi.org/10.1109/CDC.2007.4434822

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AB - We study systems in which the equilibrium point varies discontinuously according to a well defined state or time-dependent switching law. We refer to those systems as systems with switching equilibria. To motivate our study, we describe a class of problems in engineering and biology that can be formulated using such systems. We study stability and convergence properties of those systems under various switching rules. In particular we prove convergence under arbitrary switching, time-dependent and state-dependent switching laws. In the time-dependent switching case we highlight connections between the relaxation theorem corresponding to differential inclusions, Pulse-Width-Modulation (PWM) and averaging theory.

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T3 - Proceedings of the IEEE Conference on Decision and Control

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Stability and convergence for systems with switching equilibria

Abstract

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