State and unknown input estimation using proportional multiple integral observer for uncertain Takagi-Sugeno fuzzy systems

This paper deals with the problem of state and faults estimation for nonlinear uncertain systems described by Takagi Sugeno structures. In this work, we considered in this paper the case of actuator fault, they are considered as unknown inputs. The state and faults estimation is made using a structure of sliding mode observer where multiple integral term is added. This structure of observer named proportional multiple integral sliding mode observer. An adaptive mathematical form is used for the sign function to facilitate the determination of the proportional gains of the conceived observer. The integration of multiple integrals action ensures great precision to the fault estimation. The observer convergence conditions are formulated in LMI form allowing to compute the observer gains. The proposed sliding mode observer is applied in the case of a numerical example showing the efficiency of the fault and state estimation.