Noise-input-to-state stability analysis of switching stochastic nonlinear systems with mode-dependent multiple impulses

Abstract

In this study, the problem of noise-input-to-state stability for switching stochastic nonlinear systems with impulses is investigated. There are two outstanding features of the investigated systems: (a) the occurrences of swithcings and impulses are allowed to be asynchronous; (b) the impulsive maps not only depend on the subsystems but also are different for the different impulsive instants. The noise-input-to-state stability problem is first considered for systems, where switching instants and impulsive intervals are confined by the mode-dependent average dwell time and impulsive interval, respectively. Then, we revisit the noise-input-to-state stability for nonlinear systems with stochastic switching and impulsive densities. To derive less conservative sufficient conditions, multiple Lyapunov functions with the indefinite weak infinitesimal generator and some fundamental stochastic techniques are applied. A simulation example is proposed to illustrate the effectiveness of the provided criteria.