Robust adaptive proportional integral observer for faults estimation: Application to Bioreactor

In this work, we focus on state and both sensor and actuator fault (SAF) estimations for Takagi-Sugeno (T-S) fuzzy systems in the presence of an Unknown Bounded Disturbance (UBD). To reach this objective, we design a novel observer to estimate simultaneously state and SAF vectors. Indeed, we study the robustness against disturbance by considering the $H_{\infty}$ performance. For the stability, sufficient conditions are given in term of relaxed Linear Matrix Inequalities $(LLIs)$ where the descriptor formulation is considered. To prove the efficiency of our proposed method, a reduced bioreactor model and simulation results are illustrated.