Stability analysis of discrete-time switched systems via Multi-step multiple Lyapunov-like functions

被引：38
|
作者：
Lu, Junjie [1 ,2 ,3 ]
She, Zhikun [1 ,2 ]
Ge, Shuzhi Sam [3 ]
Jiang, Xin [1 ,2 ]
机构：
[1] Beihang Univ, LMIB, SKLSDE, Beijing, Peoples R China
[2] Beihang Univ, Sch Math & Syst Sci, Beijing, Peoples R China
[3] Natl Univ Singapore, Dept Elect & Comp Engn, Singapore, Singapore
来源：
NONLINEAR ANALYSIS-HYBRID SYSTEMS | 2018年 / 27卷
关键词：
Switched systems; Stability; Asymptotic stability; Multiple Lyapunov-like functions; Multi-step MLFs; LINEAR-SYSTEMS; STABILIZABILITY; COMMON; COMPUTATION; SUFFICIENT; CRITERIA; THEOREM; TARGET;
D O I：
10.1016/j.nahs.2017.07.004
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 propose a Multi-step multiple Lyapunov-like functions (MLFs) based approach to prove the stability and asymptotic stability of discrete-time switched systems under pre-given time-dependent switching signals. We start with the definition of Multi-step MLFs, which is a relaxation of traditional MLFs. Then, for a discrete-time switched nonlinear system (SNS) under a given time-dependent switching signal, several sufficient conditions for its stability and asymptotic stability are successively provided by using either Multi-step MLFs or strengthened Multi-step MLFs, respectively. Afterwards, for a discrete-time switched linear system with a special time-dependent switching signal, we derive two less conservative linear matrix inequality based criteria for demonstrating its asymptotic stability. In the end, three examples are given to illustrate the applicability and advantage of our relaxed results. (C) 2017 Elsevier Ltd. All rights reserved.
引用
收藏
页码：44 / 61
页数：18
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