Robust filtering for systems with stochastic non-linearities and deterministic uncertainties

In this paper, the robust finite-horizon filter design problem is considered for a class of discrete time-varying systems with both stochastic non-linearities and deterministic uncertainties. The description of the stochastic non-linearities is quite general, which comprises state-multiplicative noises and random sequences whose powers depend on either the sector-bound non-linear function of the state or the sign of a non-linear function of the state. The norm-bounded parameter uncertainties are allowed to enter both the system and the output matrices. The aim is to design a robust filter that guarantees an optimized upper bound on the state estimation error variance for all stochastic non-linearities and admissible deterministic 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 Ricatti-like difference equations. A numerical simulation example is presented to show the applicability of the proposed method.