Stability analysis of reentry constrained switched system based on Büchi automata

This paper considers global exponential stabilization (GES) of switched linear discrete-time system under language constraint which is generated by B chi automata. Firstly, the characteristics of the acceptable conditions of B chi automata are considered, which are used to generate the re-entry constrained switching sequences, and the global exponential stability of B chi automata is proposed. Then, by combining multiple Lyapunov functions with the initial state and acceptable state of B chi automata, a sufficient condition for the global exponential stability of the system with step decreasing Lyapunov functions is given. This condition can also be used to study the stability of Muller automata constrained switched systems.