LMI Solution for Local Nonquadratic H∞ Filter Design of Continuous-time T-S Fuzzy Systems

This paper is concerned with the nonquadratic H-infinity filter design problem for continuous-time Takagi-Sugeno (T-S) fuzzy systems. Attention is focused on the design of a stable filter guaranteeing a prescribed noise attenuation level in the H-infinity sense. In order to derive less conservative results, conditions for designing H-infinity filter are established based on a relaxed approach in which both Finsler's Lemma and nonquadratic Lyapunov function are used. The well known problem of handing timederivatives of membership functions (MFs) is overcomed by reducing global goals to the estimation of region of attraction. It is shown that conditions for the solvability of the H-infinity filter design are written in the form of linear matrix inequality (LMI) which can be efficiently solved by convex optimization techniques. Simulation example is given to demonstrate the validity of the proposed approach.