Observer-Based H∞ Control for Stochastic Systems with Delays and Nonlinear Perturbations: LMI Approach ?

This paper considers the problem of observer-based H∞ control for a class of Itôtype stochastic delay systems with nonlinear perturbations. An observer-based controller is constructed based on Lyapunov-Krasovskii approach, which guarantees the closed-loop system is robustly stochastically asymptotically stable in the mean square with prescribed H∞ disturbance attenuation level for all admissible nonlinear perturbations. Sufficient condition for the existence of desired controller is presented in terms of a strict linear matrix inequality (LMI) if the control matrix B is full column rank. A numerical example is provided to demonstrate the effectiveness of the proposed method.