Sensor Faults Observer Design with H∞ Performance for Non-linear T-S systems

This paper deals with the problem of the state estimation and the sensor faults detection for nonlinear perturbed systems described by Takagi-Sugeno (T-S) fuzzy models with unmeasurable premise variables. Indeed, a T-S 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 T-S model with unmeasurable premise variables is reduced to a perturbed model with measurable variables. Convergence conditions are established with Lyapunov theory and the H ∞ performance in order to guarantee the best robustness to disturbances. These conditions are expressed in terms of linear matrix inequalities (LMIs). The parameters of the observer are computed using the solution of the LMI conditions. Finally, a numerical example is given to illustrate the design procedures. Simulation results show the satisfactory performances.