Stability of two-time scale linear stochastic hybrid systems

The problem of exponential mean-square stability of two-time scale, linear stochastic hybrid systems has been studied in this paper. To obtain the sufficient conditions of stability, two basic approaches of stability analysis: for one-time hybrid systems with a Markovian switching rule as well as switching rule and singularly perturbed nonhybrid systems, were combined. The Lyapunov techniques were used in both approaches.