A Note on Sufficient Conditions of Almost Sure Exponential Stability for Semi-Markovian Jump Stochastic Systems

In this paper, we are concerned with the stability analysis of stochastic systems switched by the ergodic semi-Markovian process. The sufficient conditions for almost sure exponential stability are derived by using the method of multiple Lyapunov functions and the ergodic property of the semi-Markov process. Particularly, our results generalize and improve some published results in the literature. An example is presented to illustrate the effectiveness of the obtained results.