Finite Frequency H₋/H_∞ Memory Fault Detection Filtering Design for Uncertain Takagi-Sugeno Fuzzy Affine Systems

This paper is concerned with the finite frequency H₋/H_∞ memory fault detection filtering problem for discrete-time Takagi-Sugeno (T-S) fuzzy affine systems with norm-bounded uncertainties. The objective is to design a piecewise affine memory filter by using system historical information such that the resulting closed-loop filtering error system is asymptotically stable with the prescribed finite frequency H₋/H_∞ performance. Based on the generalized Kalman-Yakubovič-Popov (GKYP) lemma combined with the celebrated S-procedure, new sufficient conditions for the fuzzy affine filtering error system to have the finite frequency H₋/H_∞ performance are given at first. By further using piecewise fuzzy quadratic Lyapunov functions (PFQLFs) and Projection lemma, the filtering analysis results for the filtering error system to be asymptotically stable with the prescribed finite frequency H-/H∞ performance are obtained. Then the filtering synthesis is carried out with the aid of matrix inequality convexification techniques, and the synthesis results are described in terms of linear matrix inequalities (LMIs). It is further shown that better filtering performance can be achieved by using more system historical information. Finally, simulation is provided to verify the effectiveness of the proposed approach.