Abstract
In this paper we establish an H∞ filtering theory for discrete-time stochastic systems with uncertainties of a stochastic nature. In particular, we model the uncertain part of the system as a white noise. The theory which is developed in this paper is based on the concept of stochastic dissipativity. It is shown in this paper that stochastic dissipation yields a stochastic Bounded Real Lemma (BRL) which is the basis for the filtering theory developed in this paper. A necessary and sufficient conditions for the existence of a solution to the filtering problem are established. The issue of feasible solutions is discussed and sufficient conditions for a feasible solution to the filtering problem are given in terms of matrix inequalities.
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