Fault Detection Filtering Design for Discrete-Time Interval Type-2 T–S Fuzzy Systems in Finite Frequency Domain

This article focuses on the problem of fault detection filtering design for discrete-time interval type-2 Takagi-Sugeno (T-S) fuzzy systems in finite frequency domain. Considering the fact that external disturbances and faults are usually reside in finite frequency ranges, the finite frequency H _∞ and H _- performances are introduced to reflect the disturbance robustness and fault sensitiveness in finite frequency domain, respectively. Based on discrete-time Fourier transform and its properties, finite frequency performance analysis results are first obtained. Then, by exploiting the information on upper and lower membership functions, the membership-function-dependent filtering design conditions in the form of linear matrix inequalities are established for discrete-time interval type-2 T-S fuzzy systems in finite frequency domain. With the obtained filter, a fault detection scheme is then proposed and it is shown that the resulting fault detection system is asymptotically stable with prescribed finite frequency H _∞ and H _- performances. Finally, the effectiveness of the proposed method is validated by simulation studies.