H_/H ∞ fault detection Proportional Integral observer for uncertain T-S fuzzy systems

In this work, we investigate the detection and estimation problems of Sensor and Actuator Faults (SAF) for uncertain nonlinear systems represented by Takagi-Sugeno (TS) fuzzy models subject to an Unknown Bounded Disturbance (UBD). For this, we design a Proportional Integral (PI) observer to estimate state and both sensor and actuator fault vectors, simultaneously. To maximize the fault detection and to minimize the disturbance effects, we consider the H_/H ∞ multiobjective performances. By solving a set of Linear Matrix Inequalities (LMIs) and using Lyapunov theory, we prove the existence of this observer and we guarantee the convergence of both the state estimation errors and fault estimation errors. The descriptor formulation is used to get relaxed LMIs. Finally, a numerical example and simulation results are illustrated to prove the mentioned process efficiency.