Stability analysis of Markov switched stochastic differential equations with both stable and unstable subsystems

This paper discusses the asymptotic stability of Markov switched stochastic differential equations. By using the method of multiple Lyapunov functions, we provide sufficient conditions for stochastic asymptotic stability of Markov switched stochastic differential equations with both stable and unstable subsystems via the inequality based on the multiple Lyapunov functions and the stationary distribution of Markovian switching process. Particularly, our results include some existing results as special cases and improve some results in the literature. Two examples are given to illustrate the effectiveness of the obtained results.