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

Matthew Philippe (1) , Gilles Millérioux (2) , Raphael Jungers (1)

1 UCL - Université Catholique de Louvain = Catholic University of Louvain
2 CRAN - Centre de Recherche en Automatique de Nancy

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.

Mots clés: Dead-beat stability; Switching systems; Automata; Irreducibility; Boundedness

Domaines: Optimisation et contrôle [math.OC]; Automatique / Robotique

Matthew Philippe, Gilles Millérioux, Raphael Jungers. Deciding the boundedness and dead-beat stability of constrained switching systems. Nonlinear Analysis: Hybrid Systems, 2017, 23, pp.287-299. ⟨10.1016/j.nahs.2016.03.001⟩. ⟨hal-01320957⟩