Robust Filtering for Systems with Stochastic

In this paper, we consider the robust finite-horizon filter design problem for a class of discrete time­ varying systems with both stochastic nonlinearities and deterministiG uncertainties. The description of the stochastic nonlinearities is quite general, which comprises the state-multiplica tive noises and the ran­ dom sequences whose powers depend on either the sector-bound nonlinear function of the state or the sign of a nonlinear function of the state. The norm-. bounded parameter uncertainties are allowed to en­ ter both the system and the output matrices. We aim to design a robust filter that guarantees an optimized upper bound on the state estimation enor variance, for all stochastic nonli nearities and admissible de­ terministic uncertainties. The existence conditions for the desired robust filters are first derived, and the filter parameters are then determined in terms of the solutions to two recursive Riccati-like differ­ ence equations. A numerical example is presented to show the applicability of the proposed method.