Stability of switched systems: a Lie-algebraic condition

被引：512

作者：

Liberzon, D ^{[1
]}

Hespanha, JP ^{[1
]}

Morse, AS ^{[1
]}

机构：

[1] Yale Univ, Dept Elect Engn, New Haven, CT 06520 USA

来源：

SYSTEMS & CONTROL LETTERS | 1999年 / 37卷 / 03期

基金：

美国国家科学基金会;

关键词：

switched system; uniform exponential stability; quadratic common Lyapunov function;

D O I：

10.1016/S0167-6911(99)00012-2

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We present a sufficient condition for asymptotic stability of a switched linear system in terms of the Lie algebra generated by the individual matrices. Namely, if this Lie algebra is solvable, then the switched system is exponentially stable for arbitrary switching. In fact, we show that any family of linear systems satisfying this condition possesses a quadratic common Lyapunov function. We also discuss the implications of this result for switched nonlinear systems. (C) 1999 Elsevier Science B.V. All rights reserved.

引用

页码：117 / 122

页数：6

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