Stability of Hybrid Impulsive and Switching Stochastic Systems with Time-delay

This paper investigates a model of hybrid impulsive and switching stochastic systems (HISSS) with time-delay. Several stability criteria, including the globally asymptotical and exponential stability criteria in the pth moment and mean square, are established by using Itô formula, a generalized switching Lyapunov functions and some relating techniques. Especially, a more general Lyapunov-Krasivskii functional is constructed, and it is observed that the mean square asymptotic and exponential stability conditions of HISSS are delay-dependent. A numerical example shows that the obtained stability results can reduce the conservativeness.