Observer design for fault diagnosis for the Takagi-Sugeno model with unmeasurable premise variables

This paper deals with the problem of the state estimation and the sensor faults detection for discrete time nonlinear systems described by Takagi-Sugeno (TS) fuzzy models with unmeasurable premise variables. Indeed, a TS observer is synthesized, in descriptor form, to estimate both the system states and the sensor faults simultaneously. The idea of the proposed approach is to introduce the sensor fault as an auxiliary variable in the state vector. Besides, the multiple model with unmeasurable premise variables is reduced to a perturbed model with measurable variables. Convergence conditions are established with Lyapunov theory and the L₂ optimization in order to guarantee the convergence of the state estimation error. These conditions are expressed in terms of Linear Matrix Inequalities (LMIs). The gains matrices of the multi-observers are characterized using the solution existence of the LMI conditions. Finally, the model of an hydraulic system with three tanks is used to validate the proposed approach.