Design of robust adaptive observer for nonlinear TS fuzzy system with unknown inputs

This paper deals with robust estimation of states and unknown inputs for a class of non linear system described by Takagi-Sugeno fuzzy models. The proposed approach is developed on the basis of adaptive Luenberger observer theory. A robustness study, using the L₂ technique, is carried out to take in consideration the model uncertainties. Unknown inputs estimation is ensured through a fuzzy proportional integral adaptive law, computed from an accurate observer outputs which allow a fast dynamic estimation. Design conditions are formulated into Linear Matrix Inequalities (LMIs) terms. Numerical example is given to illustrate the efficiency of the proposed techniques.