Deciding the boundedness and dead-beat stability of constrained switching systems

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• 作者：Matthew Philippe^a ; ^{matthew.philippe@uclouvain.be} ; Gilles Millerioux^b ; ^{gilles.millerioux@univ-lorraine.fr} ; Raphaë ; l M. Jungers^a ; ^{raphael.jungers@uclouvain.be}
• 关键词：Switching systems ; Automata ; Irreducibility ; Boundedness ; Dead-beat stability
• 刊名：Nonlinear Analysis: Hybrid Systems
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：23
• 期：Complete
• 页码：287-299
• 全文大小：472 K
• 卷排序：23

文摘

We study computational questions related with the stability of discrete-time linear switching systems with switching sequences constrained by an automaton.We first present a decidable sufficient condition for their boundedness when the maximal exponential growth rate equals one. The condition generalizes the notion of the irreducibility of a matrix set, which is a well known sufficient condition for boundedness in the arbitrary switching (i.e. unconstrained) case.Second, we provide a polynomial time algorithm for deciding the dead-beat stability of a system, i.e. that all trajectories vanish to the origin in finite time. The algorithm generalizes one proposed by Gurvits for arbitrary switching systems, and is illustrated with a real-world case study.