Input-to-state stability for switched stochastic nonlinear systems with mode-dependent random impulses

This paper investigates the input-to-state stability (ISS) and integral input-to-state stability (iISS) of switched stochastic nonlinear systems with time delays and random impulses. Different from the existing researches on ISS and iISS, random impulses with both high intensity and density are taken into account. More practically, these impulses are of different stochastic characteristics with respect to different subsystems, and may also occur in coincidence with the subsystem switching instants. The upper bound of the time-derivative operator of Lyapunov function is assumed to be time-varying and mode-dependent, and some sufficient conditions for the ISS and iISS properties of this presented switched stochastic nonlinear systems are established by employing Lyapunov-Razumikhin technique and comparison principle. Finally, several numerical examples are adopted to verify the theoretical analysis.