Robust adaptive observer design for fast fault estimation for nonlinear T-S fuzzy systems using descriptor approach

In this work, we study the detection and estimation problem of sensor and actuator faults (SAF) for nonlinear systems represented by Takagi-Sugeno (T-S) fuzzy models subject to an Unknown Bounded Disturbance (UBD). Simultaneously, we study the estimation of the states. To do this, we design an adaptive descriptor observer to jointly estimate state and SAF vectors. This observer not only lead to estimate the actuator fault, but also to improve the performance of fault estimation. To prove the existence of this observer, two sufficient conditions are deduced in form of Linear Matrix Inequalities (LMIs) using Lyapunov theory. A robustness to disturbance is elaborated by considering the H ∞ performance. Finally, a numerical example and simulation results are afforded to prove the mentioned process efficiency.