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Language constrained stabilization of discrete-time switched linear systems: an LMI approach

Abstract : The goal of this paper is to study sufficient conditions to stabilize an autonomous discrete-time switched system, for which the switching law should belong to a constrained language characterized by a nondeterministic automaton. Based on a decomposition into strongly connected components of the automaton, it is shown that it suffices to consider only a nontrivial strongly connected component. Sufficient conditions are provided as a set of Linear Matrix Inequalities (LMIs) related to the automaton states and associated with a min-switching strategy. Equivalence with the periodic stabilization is investigated. A numerical example is provided to illustrate the main result.
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Submitted on : Wednesday, July 22, 2020 - 9:38:27 AM
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Marc Jungers, Antoine Girard, Mirko Fiacchini. Language constrained stabilization of discrete-time switched linear systems: an LMI approach. 6th IFAC Conference on Analysis and Design of Hybrid System, ADHS 2018, Jul 2018, Oxford, United Kingdom. ⟨10.1016/j.ifacol.2018.08.005⟩. ⟨hal-01899003⟩

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