Fuzzy H∞ filter design for a class of nonlinear discrete-time system with time delays

This paper studies fuzzy H_∞ filter for signal estimation of nonlinear discrete-time systems with time delays and unknown bounded disturbances. First, the Takagi and Sugeno (T-S) fuzzy model is proposed to represent the state-space model for a nonlinear discrete-time system with time delays. Next, we design a stable fuzzy H_∞ filter based on T-S fuzzy model, which assures asymptotic stability and a prescribed H_∞ index for the filtering error system. Sufficient condition for the existence of such a filter is established in terms of linear matrix inequality problem (LMIP). The LMIP can be efficiently solved using convex optimization techniques with global convergence guaranteed, such as the interior point algorithm. Simulation example is made to illustrate the efficiency of the proposed method.