Fuzzy $H_\infty$ Filter Design for a Class of Nonlinear Discrete-Time Systems With Multiple Time Delays

This paper studies the fuzzy H
_infin
filter design problem for signal estimation of nonlinear discrete-time 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 nonlinear discrete-time systems with 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 is established by using the linear matrix inequality (LMI) approach. The proposed LMI problem can be efficiently solved with global convergence guarantee using convex optimization techniques such as the interior point algorithm. Simulation examples are provided to illustrate the design procedure of the present method.