Faults diagnosis based on proportional integral observer for TS fuzzy model with unmeasurable premise variable

In this work, we focus on the synthesis of a Proportional Integral (PI) observer for the actuators and sensors faults diagnosis based on Takagi-Sugeno (TS) fuzzy model with unmeasurable premise variables. The faults estimation method is based on the assumption that these faults act as unknown inputs under polynomials form whose their kth derivatives are bounded. The convergence conditions of the observer as well as the faults reconstruction are established on the basis of the Lyapunov stability theory and the L₂ optimization technique, expressed as Linear Matrix Inequalities (LMI) constraints. In order to validate the proposed approach, a hydraulic system with two tanks is proposed.