Fault Detection for T–S Fuzzy Systems With Unknown Membership Functions

This paper is concerned with the fault detection (FD) problem for Takagi-Sugeno (T-S) fuzzy systems with unknown membership functions. If the membership functions are unknown, the linear FD filter designs with fixed gains have been considered in the literature. To reduce the conservatism of the existing results, a switching mechanism that depends on the lower and upper bounds of the unknown membership functions is provided to construct an FD filter with varying gains. It is shown that the switching-type FD filter with varying gains can achieve a better FD performance than the linear FD filter with fixed gains. In addition, based on some time-domain inequalities, a novel weighting matrix design approach is introduced to transform the fault sensitivity specification into an H∞ constraint. Finally, two examples are given to show the advantages of the proposed FD method.