Language constrained stabilization of discrete-time switched linear systems: a Lyapunov-Metzler inequalities approach

This paper addresses the issue of stabilizability of an autonomous discrete-time switched system via a switching law that is constrained to belong to a language generated by an nondeterministic finite state automaton. Firstly the automaton is decomposed into strongly connected components to reduce the problem to the stabilizability of each non trivial strongly connected component. Secondly the approach considering Lyapunov-Metzler inequalities taking into account the language constraint for a strongly connected component is proposed. Links with the current literature are discussed and a detailed example is given to illustrate our contributions.