Exponential stabilization for nonlinear switched stochastic systems with interval time-varying delay under asynchronous switching

The paper investigates mean-square exponential stabilization for a class of nonlinear switched stochastic systems with interval time-varying delay under asynchronous switching. Specifically, the delay occurs not only in the state equation, but also in the switching signal from the controller, which brings the difficulty of controller design to achieve mean-square exponential stabilization. Based on the Lyapunov stability theory, a new piecewise multi-Lyapunov–Krasovskii functional dependent on the size of time delay is constructed. By utilizing the matrix inequality technique and the average dwell time approach, delay-dependent sufficient conditions are given to guarantee mean-square exponential stabilization for nonlinear switched stochastic systems under asynchronous switching. In accordance with the method, we also design state feedback controllers of the switched stochastic systems under asynchronous switching through special operations of matrices and Schur complement. Finally, a numerical example and a practical example of river pollution control are provided to show the effectiveness of the approach proposed in this paper.