Exponential stabilization of discrete-time switched linear systems

被引：113

作者：

Zhang, Wei ^{[1
]}

Abate, Alessandro ^{[2
]}

Hu, Jianghai ^{[1
]}

Vitus, Michael P. ^{[2
]}

机构：

[1] Purdue Univ, Dept Elect & Comp Engn, W Lafayette, IN 47906 USA

[2] Stanford Univ, Dept Aeronaut & Astronaut, Stanford, CA 94305 USA

来源：

AUTOMATICA | 2009年 / 45卷 / 11期

基金：

美国国家科学基金会;

关键词：

Switched systems; Piecewise quadratic Lyapunov functions; Switching stabilization; Optimal control; Control-Lyapunov functions; QUADRATIC STABILIZATION; STABILITY; CRITERIA; DESIGN;

D O I：

10.1016/j.automatica.2009.07.018

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 article studies the exponential stabilization problem for discrete-time switched linear systems based on a control-Lyapunov function approach. It is proved that a switched linear system is exponentially stabilizable if and only if there exists a piecewise quadratic control-Lyapunov function. Such a converse control-Lyapunov function theorem justifies many of the earlier synthesis methods that have adopted piecewise quadratic Lyapunov functions for convenience or heuristic reasons. In addition, it is also proved that if a switched linear system is exponentially stabilizable, then it must be stabilizable by a stationary suboptimal policy of a related switched linear-quadratic regulator (LQR) problem. Motivated by some recent results of the switched LQR problem, an efficient algorithm is proposed, which is guaranteed to yield a control-Lyapunov function and a stabilizing policy whenever the system is exponentially stabilizable. (C) 2009 Elsevier Ltd. All rights reserved.

引用

页码：2526 / 2536

页数：11

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