Simultaneous state and fault estimation: A prescribed-time unknown input observer approach

In this paper, a prescribed-time unknown input observer (PTUIO) is developed for the simultaneous state and fault estimation. Firstly, for the uncertain system containing both the actuator fault and the sensor fault, a series of reformulations are proposed, which provides a more straightforward way to estimate the state and the faults. Subsequently, based on the reformulations, a PTUIO is developed such that the state, the actuator fault and the sensor fault can all be estimated within an arbitrarily prescribed time regardless of what the initial conditions are. In addition, the necessary and sufficient conditions for the existence of the PTUIO are given in terms of the original system matrices. Finally, a numerical example is given to verify the effectiveness of the proposed method.