A robust fault detection design for uncertain Takagi–Sugeno models with unknown inputs and time-varying delays

This paper investigates the problem of robust fault detection system design for a class of uncertain Takagi–Sugeno (T–S) models. The system under consideration is subject to unknown input and time-varying delay. The fault detection system is designed such that the unknown input is thoroughly decoupled from residual signals generated by the fault detection system. Furthermore, the residual signals show the maximum possible sensitivity to the faults and the minimum possible sensitivity to the external disturbances. The model matching approach is utilized to tackle the effects of parametric uncertainties in the model of the system. The design procedure is presented in terms of Linear Matrix Inequalities (LMIs). Some remarks are given to analyze the proposed method. Finally, a numerical example is presented to show the effectiveness of the proposed method.