Robust stability conditions for switched linear systems: Commutator bounds and the ojasiewicz inequality

Yuliy Baryshnikov, Daniel Liberzon

研究成果: Chapter in Book/Report/Conference proceedingConference contribution

1 被引用数 (Scopus)

抄録

This paper discusses conditions for stability of switched linear systems under arbitrary switching, formulated in terms of smallness of appropriate commutators of the matrices generating the switched system. Such conditions provide robust variants of well-known stability conditions requiring these commutators to vanish and leading to the existence of a common quadratic Lyapunov function. The main contribution of the paper is to apply the ojasiewicz inequality to characterize the persistence of a common quadratic Lyapunov function as the matrices are perturbed so that their commutators no longer vanish but instead are sufficiently small. It is shown how known constructions of common quadratic Lyapunov functions for commuting matrices and for matrices generating nilpotent or solvable Lie algebras can be used, in conjunction with the ojasiewicz inequality, to estimate allowable deviations of the commutators from zero.

本文言語英語
ホスト出版物のタイトル2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013
出版社Institute of Electrical and Electronics Engineers Inc.
ページ722-726
ページ数5
ISBN(印刷版)9781467357173
DOI
出版ステータス出版済み - 1 1 2013
外部発表はい
イベント52nd IEEE Conference on Decision and Control, CDC 2013 - Florence, イタリア
継続期間: 12 10 201312 13 2013

出版物シリーズ

名前Proceedings of the IEEE Conference on Decision and Control
ISSN(印刷版)0191-2216

その他

その他52nd IEEE Conference on Decision and Control, CDC 2013
国/地域イタリア
CityFlorence
Period12/10/1312/13/13

All Science Journal Classification (ASJC) codes

  • 制御およびシステム工学
  • モデリングとシミュレーション
  • 制御と最適化

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