Converse Lyapunov Theorems for Discrete-Time Switching Systems With Given Switches Digraphs

被引：15
|
作者：
Pepe, Pierdomenico [1 ]
机构：
[1] Univ Aquila, Ctr Excellence Res DEWS, Dept Informat Engn Comp Sci & Math, I-67100 Laquila, Italy
来源：
IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2019年 / 64卷 / 06期
关键词：
Converse Lyapunov theorems; discrete-time switching systems; global asymptotic stability; input-to-state stability; switches digraphs; TO-STATE STABILITY; OUTPUT STABILITY; DESIGN; STABILIZATION;
D O I：
10.1109/TAC.2018.2867166
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
It is proved in this paper that the existence of suitable multiple Lyapunov functions is a necessary and sufficient condition for a discrete-time nonlinear switching system, with given switches digraph, to be globally asymptotically stable. The same result is provided for the input-to-state stability. The less is the number of edges in the switches digraph, the less is the number of inequalities that are involved in the provided necessary and sufficient Lyapunov conditions.
引用
收藏
页码：2502 / 2508
页数：7
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