Asymptotic Stability in Distribution of nonlinear Stochastic Systems with Semi-Markovian Switching

Recently, some results on the stability in distribution of nonlinear stochastic differential equations with Markovian switching has been reported. However, because the distribution of Markovian chain is exponential, which limits its scope of application, there are many restrictions for the existing results in practical applications. In this paper, the problem of asymptotic stability in distribution of nonlinear stochastic systems with semi-Markovian switching is considered and some similar results as in the full-Markovian switching are obtained, which are less conservative, thus has wider application domains. An example is given to show the application potential of the proposed techniques