Fuzzy approach to H∞ filtering for delayed nonlinear stochastic systems

This paper is concerned with the infinite horizon H_∞ filtering problem for nonlinear stochastic systems with time-delay. For general delayed nonlinear stochastic systems, the conditions of H_∞ filtering are usually given in terms of Hamilton-Jacobi inequalities (HJIs), which are difficult to solve. In this paper, the delayed nonlinear stochastic systems are modeled based on the T-S fuzzy model. The exponential mean square H_∞ filter of delayed nonlinear stochastic systems is proposed via solving a set of linear matrix inequalities (LMIs) instead of HJIs. A numerical example is presented to show the effectiveness of the proposed method.