H-Infinity Filtering for Nonlinear Stochastic Systems

In this paper we develop an H_infin filtering theory, from the dissipation point of view, for a large class of time-continuous stochastic nonlinear systems. In particular, we use the notion of stochastic dissipative systems analogously to the familiar notion of dissipation associated with deterministic systems and utilize it as a basis for the development of our theory. We first establish a connection between what is called the l₂-gain property and the solution to a certain Hamilton-Jacobi inequalities (HJI), that may be viewed as a bounded real lemma for stochastic nonlinear systems. The infinite time horizon is also considered, where for this case we synthesize a worst case based stable filter which operates on the observation. Stability in this case is taken to be both in the mean-square sense and in probability. The problem of robust filtering is considered in the case of norm-bounded uncertainties. A solution is then derived in terms of linear matrix inequalities