Membership-Function-Dependent Fault Detection Filtering Design for Interval Type-2 T–S Fuzzy Systems in Finite Frequency Domain

This article studies the problem of finite frequency fault detection filtering design for uncertain nonlinear systems based on interval type-2 Takagi-Sugeno fuzzy models. It is assumed that the frequencies of disturbances and faults are in finite frequency sets, respectively. The objective is to design an admissible filter such that the fault detection system is asymptotically stable with prescribed finite frequency \mathscr H
_∞
and \mathscr H
_-
performances. Based on Fourier transform and Projection lemma, finite frequency filtering synthesis results are obtained. Then, a novel membership-function-dependent finite frequency fault detection filtering design approach is proposed by using the information of the lower and upper membership functions together with the footprint of uncertainties. Two algorithms with linear matrix inequality constraints are developed to optimize the finite frequency \mathscr H
_∞
performance and the finite frequency \mathscr H
_-
performance, respectively. Finally, simulation studies are provided to show the effectiveness of the proposed method.