Stability analysis for semi-Markovian switched stochastic systems with asynchronously impulsive jumps

Abstract

The almost surely (a.s.) exponential stability is studied for semi-Markovian switched stochastic systems with randomly impulsive jumps. We start from the case that switches and impulses occur synchronously, in which the impulsive switching signal is a semi-Markovian process. For the case that switches and impulses occur asynchronously, the impulsive arrival time sequence and the types of jump maps are driven by a renewal process and a Markov chain, respectively. By applying the multiple Lyapunov function approach, sufficient conditions of exponential stability a.s. are obtained based upon the ergodic property of semi-Markovian process. The validity of the proposed theoretical results is demonstrated by a numerical example.