Instability in time-delayed switched systems induced by fast and random switching

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:263

Article

Guo, Yao^1,2,3,4  Lin, Wei^2,3  Chen, Yuming⁴  Wu, Jianhong¹ 

[1] York Univ, Dept Math & Stat, Lab Ind & Appl Math, N York, ON M3J 1P3, Canada

[2] Fudan Univ, Sch Math Sci, LNSM, Shanghai 200433, Peoples R China

[3] Fudan Univ, Ctr Computat Syst Biol, Shanghai 200433, Peoples R China

[4] Wilfrid Laurier Univ, Dept Math, Waterloo, ON N2L 3C5, Canada

关键词: Switched system;    Random and fast switching;    Time-delay;    Stochastic instability;    Dwell time;   

DOI  :  10.1016/j.jde.2017.03.003

来源: Elsevier

【 摘 要 】

In this paper, we consider a switched system comprising finitely or infinitely many subsystems described by linear time-delayed differential equations and a rule that orchestrates the system switching randomly among these subsystems, where the switching times are also randomly chosen. We first construct a counter-intuitive example where even though all the time-delayed subsystems are exponentially stable, the behaviors of the randomly switched system change from stable dynamics to unstable dynamics with a decrease of the dwell time. Then by using the theories of stochastic processes and delay differential equations, we present a general result on when this fast and random switching induced instability should occur and we extend this to the case of nonlinear time-delayed switched systems as well. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free