Matthew Philippe

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We introduce a novel framework for the stability analysis of discrete-time linear switching systems with switching sequences constrained by an automaton. The key element of the framework is the algebraic concept ofmultinorm,which associates a different norm per node of the automaton, and allows to exactly characterize stability. Building upon this tool, we(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)
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)
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)
We study the Lp induced gain of discretetime linear switching systems with graph-constrained switching sequences. We first prove that, for stable systems in a minimal realization, for every p ≥ 1, the Lp-gain is exactly characterized through switching storage functions. These functions are shown to be the pth power of a norm. In order to consider general(More)
Our research tackles fundamental control problems on complex systems, known as cyber-physical systems, with a particular focus on the rich class known as switching systems. We show that using state-of the art optimization techniques, such as sum-of-squares programming, and taking into account the logical structure of the system, we may obtain powerful(More)
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