Exponential stabilization of discrete-time switched linear systems

被引：112
|
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
收藏
页码：2526 / 2536
页数：11
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