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

Marc Jungers | Zendy; Antoine Girard | Zendy; Mirko Fiacchini | Zendy

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

Author(s) -

Marc Jungers,

Antoine Girard,

Mirko Fiacchini

Publication year - 2018

Publication title -

ifac-papersonline

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.308

H-Index - 72

eISSN - 2405-8971

pISSN - 2405-8963

DOI - 10.1016/j.ifacol.2018.08.005

Subject(s) - nondeterministic algorithm , automaton , mathematics , discrete time and continuous time , hybrid automaton , set (abstract data type) , equivalence (formal languages) , linear matrix inequality , control theory (sociology) , computer science , discrete mathematics , mathematical optimization , theoretical computer science , statistics , control (management) , artificial intelligence , programming language

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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