Stability analysis of switched linear stochastic systems

In this paper, the stability analysis problem is considered for switched linear stochastic systems, where both stable and unstable subsystems are involved, by using the Lyapunov-like function approach. When there is a common Lyapunov-like function for all subsystems, it is shown that the switched system is globally asymptotically stable in probability (GAS-P) if the total activation time ratio of unstable subsystems to stable ones is less than a specified constant. When there is not a common Lyapunov-like function for all subsystems, the proposal is made to use the multiple Lyapunov-like function and to show that in addition to the total activation time ratio requirement, if the average dwell time is sufficiently large, then the switched stochastic system is GAS-P.