Upper and lower bounds for the maximal Lyapunov exponent of singularly perturbed linear switching systems

被引：5

作者：

Chitour, Yacine ^{[1
,4
]}

Haidar, Ihab ^{[2
]}

Mason, Paolo ^{[1
]}

Sigalotti, Mario ^{[3
]}

机构：

[1] Univ Paris Saclay, Lab Signaux & Syst, CNRS, CentraleSupelec, F-91190 Gif Sur Yvette, France

[2] ENSEA, Lab Quartz, EA 7393, Cergy Pontoise, France

[3] Sorbonne Univ, Inria, CNRS, Lab Jacques Louis Lions, Paris, France

[4] Inst Univ France IUF, Paris, France

来源：

AUTOMATICA | 2023年 / 155卷

关键词：

Switching systems; Singular perturbation; Exponential stability; Maximal Lyapunov exponent; Differential inclusions; STABILITY; PERTURBATIONS;

D O I：

10.1016/j.automatica.2023.111151

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 consider the problem of determining the stability properties, and in particular assessing the exponential stability, of a singularly perturbed linear switching system. One of the challenges of this problem arises from the intricate interplay between the small parameter of singular perturbation and the rate of switching as both tend to zero. Our approach consists in characterizing suitable auxiliary linear systems that provide lower and upper bounds for the asymptotics of the maximal Lyapunov exponent of the linear switching system as the parameter of the singular perturbation tends to zero. & COPY; 2023 Elsevier Ltd. All rights reserved.

引用

页数：12

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