Fuzzy Observer Design for Fault Estimation for Discrete-time Takagi-Sugeno Singular Models with Unmeasurable Premise Variables

Abstract

This paper aims to present a new approach in the design of observers for a Class of Discrete-time Takagi-Sugeno Singular Models (DTTSM) in the case of unmeasurable premise variables, allowing to estimate simultaneously the states of the system, and the faults in the actuators and sensors. The approach used is based on augmenting the state vector. The exponential convergence is studied using the Lyapunov theory. The stability conditions are presented as Linear Matrix Inequalities (LMIs). Lastly, a numerical application is used to evaluate the efficiency of the proposed dynamic system. It shows that the estimated variables catch up rapidly (around 0.3s), and accurately the real variables during the application time of the actuator and sensor faults.