Robust unknown input observer design for uncertain interval type-2 T-S fuzzy systems subject to time-varying delays

This paper investigates the problem of robust unknown input observers design for fault detection of Takagi-Sugeno fuzzy systems. In order to handle uncertainties related to membership functions and rule-base, in this study interval type-2 fuzzy sets are employed as activation functions. The system is supposed to be affected by parameter uncertainties and time-varying delays, which makes the design procedure more challenging. Furthermore, to achieve better results in the detection of faults, a multi-objective optimization index is considered so as to get a residual signal with the most possible sensitivity to the fault and least one to other signals. This issue will lead to some design constraints in the terms of linear matrix inequalities. Two case studies are provided to show the validity of the proposed method. In addition, the superiority of interval type-2 fuzzy sets compared to type-1 sets is investigated in the simulation part.