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

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