Abstract
The purpose of this paper is to study almost sure exponential stability (ASES) of a class of semi-Markov jump systems with/without asynchronous controller. Based on the stationary distribution and ergodicity of semi-Markov switching process, sufficient stability conditions of semi-Markov jump systems are established firstly, which significantly improved some known results. Then, the sufficient conditions of ASES for semi-Markov jump systems with asynchronous controller is investigated. To be pointed out that the stochastic Lyapunov function constructed in this paper is new, which couples the switching points of semi-Markov process and a newly defined segment bounded function. Finally, two examples are given to show the superiority of our conclusions.
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