Towards robust Lie-algebraic stability conditions for switched linear systems

Andrei A. Agrachev; Yuliy Baryshnikov; Daniel Liberzon

doi:10.1109/CDC.2010.5717603

Towards robust Lie-algebraic stability conditions for switched linear systems

Andrei A. Agrachev, Yuliy Baryshnikov, Daniel Liberzon

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

5 Citations (Scopus)

Abstract

This paper presents new sufficient conditions for exponential stability of switched linear systems under arbitrary switching, which involve the commutators (Lie brackets) among the given matrices generating the switched system. The main novel feature of these stability criteria is that, unlike their earlier counterparts, they are robust with respect to small perturbations of the system parameters. Two distinct approaches are investigated. For discrete-time switched linear systems, we formulate a stability condition in terms of an explicit upper bound on the norms of the Lie brackets. For continuous-time switched linear systems, we develop two stability criteria which capture proximity of the associated matrix Lie algebra to a solvable or a .solvable plus compact. Lie algebra, respectively.

Original language	English
Title of host publication	2010 49th IEEE Conference on Decision and Control, CDC 2010
Pages	408-413
Number of pages	6
DOIs	https://doi.org/10.1109/CDC.2010.5717603
Publication status	Published - Dec 1 2010
Externally published	Yes
Event	2010 49th IEEE Conference on Decision and Control, CDC 2010 - Atlanta, GA, United States Duration: Dec 15 2010 → Dec 17 2010

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0191-2216

Other

Other	2010 49th IEEE Conference on Decision and Control, CDC 2010
Country/Territory	United States
City	Atlanta, GA
Period	12/15/10 → 12/17/10

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Modelling and Simulation
Control and Optimization

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10.1109/CDC.2010.5717603

Cite this

Towards robust Lie-algebraic stability conditions for switched linear systems. / Agrachev, Andrei A.; Baryshnikov, Yuliy; Liberzon, Daniel.
2010 49th IEEE Conference on Decision and Control, CDC 2010. 2010. p. 408-413 5717603 (Proceedings of the IEEE Conference on Decision and Control).

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

Agrachev, AA, Baryshnikov, Y & Liberzon, D 2010, Towards robust Lie-algebraic stability conditions for switched linear systems. in 2010 49th IEEE Conference on Decision and Control, CDC 2010., 5717603, Proceedings of the IEEE Conference on Decision and Control, pp. 408-413, 2010 49th IEEE Conference on Decision and Control, CDC 2010, Atlanta, GA, United States, 12/15/10. https://doi.org/10.1109/CDC.2010.5717603

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abstract = "This paper presents new sufficient conditions for exponential stability of switched linear systems under arbitrary switching, which involve the commutators (Lie brackets) among the given matrices generating the switched system. The main novel feature of these stability criteria is that, unlike their earlier counterparts, they are robust with respect to small perturbations of the system parameters. Two distinct approaches are investigated. For discrete-time switched linear systems, we formulate a stability condition in terms of an explicit upper bound on the norms of the Lie brackets. For continuous-time switched linear systems, we develop two stability criteria which capture proximity of the associated matrix Lie algebra to a solvable or a .solvable plus compact. Lie algebra, respectively.",

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N2 - This paper presents new sufficient conditions for exponential stability of switched linear systems under arbitrary switching, which involve the commutators (Lie brackets) among the given matrices generating the switched system. The main novel feature of these stability criteria is that, unlike their earlier counterparts, they are robust with respect to small perturbations of the system parameters. Two distinct approaches are investigated. For discrete-time switched linear systems, we formulate a stability condition in terms of an explicit upper bound on the norms of the Lie brackets. For continuous-time switched linear systems, we develop two stability criteria which capture proximity of the associated matrix Lie algebra to a solvable or a .solvable plus compact. Lie algebra, respectively.

AB - This paper presents new sufficient conditions for exponential stability of switched linear systems under arbitrary switching, which involve the commutators (Lie brackets) among the given matrices generating the switched system. The main novel feature of these stability criteria is that, unlike their earlier counterparts, they are robust with respect to small perturbations of the system parameters. Two distinct approaches are investigated. For discrete-time switched linear systems, we formulate a stability condition in terms of an explicit upper bound on the norms of the Lie brackets. For continuous-time switched linear systems, we develop two stability criteria which capture proximity of the associated matrix Lie algebra to a solvable or a .solvable plus compact. Lie algebra, respectively.

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BT - 2010 49th IEEE Conference on Decision and Control, CDC 2010

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Towards robust Lie-algebraic stability conditions for switched linear systems

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