Robust Fuzzy Filter Design for a Class of Nonlinear Stochastic Systems

This paper describes the robust Hinfin fuzzy filtering design for a class of nonlinear stochastic systems. The system dynamic is modelled by Itocirc-type stochastic differential equations. For general nonlinear stochastic systems, the Hinfin filter can be obtained by solving a second-order nonlinear Hamilton-Jacobi inequality. In general, it is difficult to solve the second-order nonlinear Hamilton-Jacobi inequality. In this paper, using fuzzy approach [Takagi-Sugeno (T-S) fuzzy model], the Hinfin fuzzy filtering design for the nonlinear stochastic systems can be given via solving linear matrix inequalities (LMIs) instead of a second-order Hamilton-Jacobi inequality. When the worst-case fuzzy disturbance is considered, a near minimum variance fuzzy filtering problem is also solved by minimizing the upper bound on the variance of the estimation error. The near minimum variance fuzzy filtering problem under the worst-case fuzzy disturbance is also characterized in terms of linear matrix inequality problem (LMIP), which can be efficiently solved by the convex optimization techniques. Simulation examples are provided to illustrate the design procedure and expected performance