Delay Systems With Random Perturbations Robust H_ ¡Þ Control And Filtering

This paper considers discrete time-delay systems with stochastic perturbation in states. The model mentioned above is a particular case of the general time-delay systems for its stochastic state matrix. We mainly focus on the problems of state feedback robust control and H_∞filtering problems.First of all, we investigate mean-square asymptotic stability of the systems. The sufficient conditions of the problem are obtained. Then based on the stability result, the controllers are designed respectively to stabilize the system and satisfied corresponding H_∞performance and guaranteed cost performance. Secondly, we concern with the robust H_∞filtering for uncertain discrete-time stochastic systems with time delays. The problem we address is design of a filter which ensures stochastic stability and a prescribe H_∞performance of the filtering error systems. A sufficient condition for the solvability of this problem is obtained. A desired filter can be constructed by solving a convex optimization problem in terms of an LMI. Finally, we provide a numerical example to demonstrate the applicability of the proposed approach in each section.