Fuzzy H-Infinity Filtering of Discrete-Time Nonlinear Systems with Multiple Time Delays

In this paper, we study the fuzzy H_infin filter design problem for signal estimation of discrete-time nonlinear systems with multiple time delays and unknown bounded disturbances. First, the Takagi-Sugeno (T-S) fuzzy model is used to represent the state-space model of discrete-time nonlinear systems with multiple time delays. Next, we design a stable fuzzy H_infin filter based on the T-S fuzzy model, which guarantees asymptotic stability and a prescribed H_infin index for the filtering error system, irrespective of the time delays and uncertain disturbances. A sufficient condition for the existence of such a filter design is established by using the linear matrix inequality (LMI) approach. The present LMI problem can efficiently be solved with global convergence guarantee using existing convex optimization techniques such as the interior point algorithm. A simulation example is provided to illustrate the design procedure of the present fuzzy H_infin, filter design method