H_∞ filtering for uncertain bilinear stochastic systems

This paper is concerned with the problem of H_∞ filtering for continuous-time uncertain stochastic systems. The model under consideration contains both state-dependent stochastic noises and deterministic parameter uncertainties residing in a polytope. According to the online availability of the information on the uncertain parameters, we propose two approaches, namely robust stochastic H_∞ filtering and parameter-dependent stochastic H_∞ filtering. Both approaches solve the filtering problems based on a modified (improved) bounded real lemma for continuous-time stochastic systems, which decouples the product terms between the Lyapunov matrix and systems matrices and enables us to exploit parameter-dependent stability idea in the filter designs. Sufficient conditions for the existence of admissible robust stochastic H_∞ filters and parameter-dependent stochastic H_∞ filters are obtained in terms of linear matrix inequalities, upon which the filter designs are cast into convex optimization problems. Since the filter designs make full use of the parameter-dependent stability idea, the obtained results are less conservative than the existing one in the quadratic framework. A numerical example is provided to illustrate the effectiveness and advantage of the filter design methods proposed in this paper.