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Exponential stabilization of language constrained discrete-time switched linear systems: A geometrical approach

In this paper, the stabilizability of discrete-time linear switched systems subject to constraints on the switching law is considered. The admissible switching sequences are given by the language generated by a nondeterministic finite state automaton. An algorithm is proposed for computing contractive sets defined in the space of the continuous and finite states that induce recurrent exponential control Lyapunov functions for the system. A necessary and sufficient condition for the existence of recurrent control Lyapunov functions is given in terms of finite termination of the algorithm.