Parameter-Dependent Lyapunov Functions for Linear Systems With Constant Uncertainties

被引：7
|
作者：
Seiler, Peter [1 ]
Topcu, Ufuk [2 ]
Packard, Andy [3 ]
Balas, Gary [1 ]
机构：
[1] Univ Minnesota, Minneapolis, MN 55455 USA
[2] CALTECH, Pasadena, CA 91125 USA
[3] Univ Calif Berkeley, Berkeley, CA 94720 USA
来源：
IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2009年 / 54卷 / 10期
关键词：
Parameter-dependent Lyapunov function (PDLF); ROBUST STABILITY; QUADRATIC STABILIZABILITY; POPOV CRITERION; ATTRACTION; DOMAIN; REAL; MU;
D O I：
10.1109/TAC.2009.2029294
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
Robust stability of linear time-invariant systems with respect to structured uncertainties is considered. The small gain condition is sufficient to prove robust stability and scalings; are typically used to reduce the conservatism of this condition. It is known that if the small gain condition is satisfied with constant scalings then there is a single quadratic Lyapunov function which proves robust stability with respect to all allowable time-varying perturbations. In this technical note we show that if the small gain condition is satisfied with frequency-varying scalings then an explicit parameter dependent Lyapunov function can be constructed to prove robust stability with respect to constant uncertainties. This Lyapunov function has a rational quadratic dependence on the uncertainties.
引用
收藏
页码：2410 / 2416
页数：7
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