Stochastic Incremental Input-to-State Stability of Nonlinear Switched Systems with Brownian Motions

In this paper, (reverse) mode-dependent average dwell time (MDADT) method combined with multiple incremental Lyapunov functions is utilized to investigate the stochastic incremental input-to-state stability (SIISS) of stochastic switched systems. The sufficient conditions in terms of the (reverse) MDADT scheme are extracted to ensure SIISS, while it is shown that the SIISS can still be achieved even if all subsystems are not stochastically incrementally input-to-state stable. In particular, an incremental supply rate is introduced to obtain sufficient conditions to ensure SIISS for stochastic feedback interconnected switched systems. Specifically, when the stochastic switched systems are composed of some SIISS and non-SIISS subsystems, the (reverse) MDADT method is employed to establish a relationship between these two kinds of subsystems to ensure SIISS for the stochastic switched systems. Two examples are presented to demonstrate the effectiveness of the results.