Proportional integral sliding mode observer for uncertain Takagi Sugeno systems with unknown inputs

This paper deals with the problem of state and faults estimation for nonlinear uncertain systems described by Takagi Sugeno structures (named multiple models). In this work, only actuator are considered, they are considered as unknown inputs. The state and faults estimation is made using a structure of sliding mode observer where an integral term is added. This structure of observer is named proportional integral sliding mode observer. The integral term permits the fault estimation. The observer convergence conditions are formulated in LMI form allowing to compute the observer gains. The proposed proportional integral sliding mode observer is applied in the case of a numerical example showing the efficiency of the fault and state estimation.