Stability analysis of stochastic nonlinear switched systems with time‐delay and its application

Abstract This paper studies the stability of stochastic nonlinear time‐delay systems with arbitrary switching and its application. A novel Krasovskii‐type stability theorem is introduced for stochastic nonlinear systems featuring arbitrary switching and time‐delay. Unlike previous results, this stability result removes the restriction that the infinitesimal generator of Lyapunov–Krasovskii functional (i.e., ) must be negative definite and allows to be indefinite. As an application, the tracking control is studied for a class of stochastic switched systems with inverse dynamics and time‐delay. The assumption condition imposed on the inverse dynamic subsystem is weaker compared with most of existing findings. Finally, we illustrate the feasibility and effectiveness of proposed control strategy by two simulation examples.