Towards robust Lie-algebraic stability conditions for switched linear systems

Andrei A. Agrachev, Yuliy Baryshnikov, Daniel Liberzon

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 languageEnglish (US)
Title of host publication2010 49th IEEE Conference on Decision and Control, CDC 2010
Pages408-413
Number of pages6
DOIs
StatePublished - 2010
Event2010 49th IEEE Conference on Decision and Control, CDC 2010 - Atlanta, GA, United States
Duration: Dec 15 2010Dec 17 2010

Publication series

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

Other

Other2010 49th IEEE Conference on Decision and Control, CDC 2010
CountryUnited States
CityAtlanta, GA
Period12/15/1012/17/10

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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  • Cite this

    Agrachev, A. A., 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 (pp. 408-413). [5717603] (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2010.5717603