Filtering for a class of nonlinear discrete-time stochastic systems with state delays

In this paper, the filtering problem is investigated for a class of nonlinear discrete-time stochastic systems with state delays. We aim at designing a full-order filter such that the dynamics of the estimation error is guaranteed to be stochastically, exponentially, ultimately bounded in the mean square, for all admissible nonlinearities and time delays. First, an algebraic matrix inequality approach is developed to deal with the filter analysis problem, and sufficient conditions are derived for the existence of the desired filters. Then, based on the generalized inverse theory, the filter design problem is tackled and a set of the desired filters is explicitly characterized. A simulation example is provided to demonstrate the usefulness of the proposed design method.