Design of observers for Takagi¿Sugeno descriptor systems with unknown inputs and application to fault diagnosis

A method for state-estimation of Takagi–Sugeno descriptor systems (TSDS) affected by unknown inputs (UI) has been presented here. For ease of implementation’s sake, the proposed observers are not in descriptor form, but in usual form. Sufficient existence conditions of the unknown input observers (UIOs) are given and strict linear matrix inequalities are solved to determine the gain of the observers. If the perfect UI decoupling is not possible, the UIO is designed in order to minimise the L2-gain from the UI to the state estimation error. The two previous objectives can be mixed in order to decouple the estimation to a subset of the UI, while attenuating the L2-gain from the other UI to the estimation. The proposed UI observers are used for robust fault diagnosis. Fault diagnosis for TSDS is performed by designing a bank of observers. A simple decision logic and thresholds setting allow to determine the occurring fault. The results are established for both the continuous and the discrete time cases. The proposed method is illustrated by a numerical example.