Matthew Philippe

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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,(More)
We study the boundedness of products of matrices associated with words in a regular language. This question naturally arises in the stability analysis of switching systems with constrained switching sequences. Our main contribution is a sufficient condition for the boundedness of all the possible products of matrices that may occur in a marginally unstable(More)
A Path-Complete Lyapunov Function is an algebraic criterion composed of a finite number of functions, called pieces, and a directed, labeled graph defining Lyapunov inequalities between these pieces. It provides a stability certificate for discrete-time arbitrary switching systems. In this paper, we prove that the satisfiability of such a criterion implies(More)
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