The Set of Asymptotically Stable Switching Sequences of Linear Discrete-Time Switching Systems

被引：0
|
作者：
Huang, Yu [1 ]
Luo, Jun [1 ]
Huang, Tingwen [2 ]
Xiao, MingQing [3 ]
机构：
[1] Zhongshan Univ, Guangzhou, Guangdong, Peoples R China
[2] Texas A&M Univ, Doha, Qatar
[3] Southern Illinois Univ, Carbondale, IL 62901 USA
来源：
PROCEEDINGS OF THE 48TH IEEE CONFERENCE ON DECISION AND CONTROL, 2009 HELD JOINTLY WITH THE 2009 28TH CHINESE CONTROL CONFERENCE (CDC/CCC 2009) | 2009年
关键词：
Discrete-time switched linear systems; asymptotically stability; Hausdorff dimension; ergodic probability measure; LYAPUNOV FUNCTIONS; STABILITY ANALYSIS; DYNAMICAL-SYSTEMS; STABILIZATION;
D O I：
10.1109/CDC.2009.5399807
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 we study the characterization of asymptotic stability for discrete-time switched linear systems. We first translate the system dynamics into a symbolic setting under the framework of symbolic topology. Then by using the ergodic measure theory, a lower bound estimate of Hausdorff dimension of the set of asymptotically stable sequences is obtained. We show that the Hausdorff dimension of the set of asymptotically stable switching sequences is positive if and only if the corresponding switched linear system has at least one asymptotically stable switching sequence. The obtained result reveals a underlying fundamental principle: a switched linear system either possesses uncountable numbers of asymptotically stable switching sequences or has none of them, provided that the switching is arbitrary.
引用
收藏
页码：2162 / 2167
页数：6
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