Uniform stability of switched linear systems: Extensions of LaSalle's invariance principle

被引:689
作者
Hespanha, JP [1 ]
机构
[1] Univ Calif Santa Barbara, Dept Elect & Comp Engn, Santa Barbara, CA 93106 USA
基金
美国国家科学基金会;
关键词
hybrid systems; LaSalle's invariance principle; stability; switched systems;
D O I
10.1109/TAC.2004.825641
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
This paper addresses the uniform stability of switched linear systems, where uniformity refers to the convergence bate of the multiple solutions that one obtains as the switching signal ranges over a given set. We provide a collection of results that can be viewed as extensions of LaSalle's Invariance Principle to certain classes of switched linear systems. Using these results one can deduce asymptotic stability using multiple Lyapunov functions whose Lie derivatives are only negative semidefinite. Depending on the regularity assumptions placed on the switching signals, one may be able to conclude just asymptotic stability or (uniform) exponential stability. We show by counter-example that the results obtained are tight.
引用
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页码:470 / 482
页数:13
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