A convex approach to robust stability for linear systems with uncertain scalar parameters

被引：156

作者：

Bliman, PA ^{[1
]}

机构：

[1] Inst Natl Rech Informat & Automat, F-78153 Le Chesnay, France

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2004年 / 42卷 / 06期

关键词：

robust stability; real and complex parametric uncertainty; polytopic uncertainty; parameter-dependent Lyapunov functions; linear matrix inequalities; mu-analysis; structured singular values; Kalman-Yakubovich-Popov lemma;

D O I：

10.1137/S0363012901398691

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper, robust stability for linear systems with several uncertain (complex and/or real) scalar parameters is studied. A countable family of conditions sufficient for robust stability is given, in terms of solvability of some simple linear matrix inequalities (LMIs). These conditions are of increasing precision, and it is shown conversely that robust stability implies solvability of these LMIs from a certain rank and beyond. This result constitutes an extension of the characterization by solvability of Lyapunov inequality of the asymptotic stability for usual linear systems. It is based on the search of parameter-dependent quadratic Lyapunov functions, polynomial of increasing degree in the parameters.

引用

页码：2016 / 2042

页数：27

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