Fuzzy Observer Design for State and Fault Estimation for Takagi-Sugeno Implicit Models

Abstract

In this study, we develop a fuzzy observer for a class of discrete-time nonlinear implicit models that are described by the Takagi-Sugeno structure and affected by actuator and sensor faults with unmeasurable premise variables satisfying the Lipschitz constraints. This study is based on separating dynamic and static equations in discrete-time Takagi-Sugeno implicit models. The design of a fuzzy observer is proposed to estimate unknown states, actuators, and sensor faults simultaneously. It is designed by considering the fault variables constituted by the actuator and sensor faults as auxiliary state variables. The observer gain is calculated by studying the exponential convergence of the state estimation error using the Lyapunov theory and the stability condition given as a linear matrix inequality. Simulation results demonstrated the effectiveness and validity of the proposed method.