H∞ guaranteed cost control for a class of discrete-time stochastic systems with sector nonlinearities and mixed time delays

This paper deals with the H∞ guaranteed cost control problem for a class of discrete-time stochastic systems involving sector nonlinearities and mixed time delays. Based on the H∞ guaranteed cost control theory and Lyapunov-Krasovskii functional method, an effective approach is proposed to design a H∞ state feedback guaranteed cost controller such that the resultant closed-loop system is stochastically stable in the mean square sense and has a H∞ performance level, and obtains a specified quadratic cost upper bound. Since the conditions obtained for the existence of H∞ guaranteed cost controllers are not linear matrix inequalities, a modified cone complementarity linearization algorithm is employed to solve the non-convex feasibility control problem. A numerical example demonstrates the effectiveness of the method.