Exponential H∞ guaranteed cost control for nonlinear stochastic delay systems

This paper investigates H_infin guaranteed cost control for a class of Ito-type stochastic systems with time delays and nonlinear perturbations. Based on Lyapunov-Krasovskii method, a state-feedback guaranteed cost controller is proposed. The designed controller guarantees the resulting closed-loop system is stochastically exponentially mean-square stable with a prescribed H_infin disturbance attenuation level, for all admissible nonlinear perturbations. Sufficient condition for the existence of desired controller is formulated in terms of a linear matrix inequality (LMI). Moreover, the design problem of the optimal exponential H_infin guaranteed cost controller for the nonlinear stochastic delay systems is cast into a standard convex optimization problem with LMIs constraints. The effectiveness of the proposed method is demonstrated by a numerical example.