Stabilization of Nonlinear Switched Systems with Distributed Time-delay: The Discrete-time Case

This paper investigates the stabilization problem of nonlinear switched systems subject to the distributed time-delay. The considered nonlinear switched systems are quite general whose dynamics are affected by both exogenous noises and distributed time-delay. The purpose of the addressed problem is to propose a state feedback control law such that, the closed-loop system is exponentially stable in the mean square sense and meanwhile, the required weighted L2 gain is achieved. By resorting to the Lyapunov functional method in combination with the average dwell time approach, sufficient conditions are provided for the existence of the desired control scheme in terms of the feasibility of certain Hamilton-Jacobi inequalities (HJIs). Within the established framework, the required feedback controller gains can be obtained by solving the series of HJIs. Finally, an illustrative numerical example is provided to demonstrate the effectiveness of the developed control algorithm.