Robust fault detection design for unknown inputs Takagi-Sugeno models with parametric uncertainties and time-varying delays

This paper deals with the design of robust fault detection system for Takagi-Sugeno (T-S) modes with parametric uncertainties and time-varying delay. An Unknown Input Observer (UIO) is designed such that the unknown inputs are thoroughly decoupled from residual signals while they show the maximum possible sensitivity to the faults and the minimum possible sensitivity to the external disturbances. Since the system under consideration is subjected to parametric uncertainties, the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> model matching approach is used to design an optimal observer. Design procedure is given in terms of Linear Matrix Inequalities (LMIs). Finally, a numerical example is presented to show the effectiveness of the proposed method.