Stabilizability of linear switching systems

被引：21
|
作者：
De Santis, E. [1 ]
Di Benedetto, M. D. [1 ]
Pola, G. [1 ]
机构：
[1] Univ Aquila, Dept Elect & Informat Engn, Ctr Excellence DEWS, I-67040 Laquila, Italy
来源：
NONLINEAR ANALYSIS-HYBRID SYSTEMS | 2008年 / 2卷 / 03期
关键词：
Linear switching systems; Stabilizability; Lyapunov functions; Kalman decomposition; Hybrid systems;
D O I：
10.1016/j.nahs.2007.11.007
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
A complete characterization of stabilizability for linear switching systems is not available in the literature. In this paper, we show that the asymptotic stabilizability of linear switching systems is equivalent to the existence of a hybrid Lyapunov function for the controlled system, for a suitable control strategy. Further, we prove that asymptotic stabilizability of a switching system with minimum dwell time, is equivalent to Input to State Stability (ISS) of the controlled switching system, with a stabilizing control law. We then derive some structural reductions of the hybrid state space, which allow a decomposition of the original problem into simpler subproblems. The relationships between this approach and the well-known Kalman decomposition of linear dynamic control systems are explored. (C) 2007 Elsevier Ltd. All rights reserved.
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页码：750 / 764
页数：15
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