Robust H Infinite Filtering of Discrete Time-delay Systems with Stochastic Perturbation

This paper considers the problem of robust H_∞ filtering for uncertain discrete time-delay systems with stochastic perturbation. The model mentioned above is a particular case of the general time-delay systems for its stochastic state matrices. The problem to be addressed is the design of a filter that guarantees mean-square asymptotic stability and a prescribed H_∞ performance level of the filtering error system for all admissible uncertainties and time-delays. A sufficient condition for the existence of such filters will be obtained. And the desired filter can be constructed by solving a convex optimization problem in terms of a linear matrix inequality (LMI). Finally, an illustrative example will be provided to demonstrate the effectiveness and applicability of the proposed method.