Generalized H2/H infinity Filtering for Discrete-Time Nonlinear System with T-S Fuzzy Models

This paper investigates the generalized H₂/H_∞ filtering problem for a class of discrete-time nonlinear systems with Takagi-Sugeno fuzzy models. The purpose of the generalized H₂/H_∞ filtering is to design a filter guaranteeing prescribed noise attenuation level in both generalized H₂ and H_∞ sense. The filter design makes use of different basis-dependent Lyapunov functions respect to different performances, which can derive less conservative result than the common Lyapunov function approach does. Sufficient conditions of the solvability of the problem are given in the form of linear matrices inequality. A numerical example is presented to illustrate the effectiveness of the proposed approach.