Deciding the boundedness and dead-beat stability of constrained switching systems. (February 2017)

• Record Type: Journal Article
• Authors: Philippe, Matthew; Millerioux, Gilles; Jungers, Raphaël M.
• Is Part Of: Nonlinear analysis. Volume 23(2017)
• Page Start: 287
• Page End: 299
• Publication Date: 2017-02
• Subjects: Switching systems -- Automata -- Irreducibility -- Boundedness -- Dead-beat stability; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2016.03.001
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: 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.