T–S fuzzy affine model based non-synchronized state estimation for nonlinear Itô stochastic systems

This paper deals with the robust H∞H∞ filter design problem for a class of nonlinear stochastic systems which are modeled by uncertain Takagi–Sugeno (T–S) fuzzy affine Itô stochastic models affected by a multidimensional Wiener process. The objective is to design an admissible full-order filter so that the resulting stochastic filtering error system is mean-square asymptotically stable with a prescribed disturbance attenuation level in an H∞H∞ sense. It is assumed that the plant premise variables are not necessarily measurable so that the filter implementation with state space partition may be not synchronized with the state trajectories of the plant. Based on piecewise quadratic Lyapunov functions, some new results are proposed for the filtering design of T–S fuzzy affine Itô stochastic systems. The filter gain of each region can be obtained by solving a set of linear matrix inequalities (LMIs). Finally, two simulation examples are provided to illustrate the effectiveness of the proposed filtering design approach.