State and sensor faults estimation via a proportional integral observer

This paper deals with the problem of fault detection and identification in noisy systems. A proportionnal integral observer with unknown inputs is used to reconstruct state and sensors faults. A mathematical transformation is made to conceive an augmented system, in which the initial sensor fault appear as an unknown input. The noise effect on the state and fault estimation errors is also minimized. The obtained results are then extended to nonlinear systems described by nonlinear Takagi-Sugeno models.