On robust Lie-algebraic stability conditions for switched linear systems

Andrei A. Agrachev, Yuliy Baryshnikov, Daniel Liberzon

Research output: Contribution to journalArticle

18 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 languageEnglish
Pages (from-to)347-353
Number of pages7
JournalSystems and Control Letters
Volume61
Issue number2
DOIs
Publication statusPublished - Feb 1 2012
Externally publishedYes

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Linear systems
Stability criteria
Algebra
Electric commutators
Asymptotic stability

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Computer Science(all)
  • Mechanical Engineering
  • Electrical and Electronic Engineering

Cite this

On robust Lie-algebraic stability conditions for switched linear systems. / Agrachev, Andrei A.; Baryshnikov, Yuliy; Liberzon, Daniel.

In: Systems and Control Letters, Vol. 61, No. 2, 01.02.2012, p. 347-353.

Research output: Contribution to journalArticle

Agrachev, Andrei A. ; Baryshnikov, Yuliy ; Liberzon, Daniel. / On robust Lie-algebraic stability conditions for switched linear systems. In: Systems and Control Letters. 2012 ; Vol. 61, No. 2. pp. 347-353.
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