On stability of discrete-time switched systems

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• 作者：Atreyee Kundu^a ; ^{atreyee.kundu@univ-lorraine.fr} ; Debasish Chatterjee^b ; ^{dchatter@iitb.ac.in}
• 关键词：Switched systems ; Global asymptotic stability ; Input/output-to-state stability ; Multiple Lyapunov-like functions ; Graph theory
• 刊名：Nonlinear Analysis: Hybrid Systems
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：23
• 期：Complete
• 页码：191-210
• 全文大小：610 K
• 卷排序：23

文摘

This article deals with stability of discrete-time switched systems. Given a family of nonlinear systems and the admissible switches among the systems in the family, we first propose a class of switching signals under which the resulting switched system is globally asymptotically stable. We allow unstable systems in the family and our stability condition depends solely on asymptotic behaviour of the switching signals. We then discuss algorithmic construction of the above class of switching signals, and show that in the presence of exogenous inputs and outputs, a switching signal so constructed also ensures input/output-to-state stability for discrete-time switched nonlinear systems. We finally show that our class of switching signals that ensures global asymptotic stability also extends to the continuous-time setting with minor modifications under standard assumptions. We employ multiple Lyapunov-like functions and graph theoretic tools as the main apparatuses for our analysis.