Prescribed-time observer for descriptor systems with unknown input

This paper investigates the problem of simultaneous state and unknown input estimation/observation within a prescribed time for a class of descriptor systems with unknown inputs (UIs). Firstly, for the descriptor system with UIs, a new structure decomposition is developed which provides a more straightforward way to estimate the state and UIs. Subsequently, based on the sub-system obtained by the decomposition, new prescribed time unknown input observers (PTUIOs) are developed for both the single-output and the multiple-output cases, which, on the one hand, achieves the simultaneous state and UI estimation within an arbitrarily prescribed time, and on the other hand, breaks through the restriction imposed in the literature that the sub-system should be single-output and meanwhile be in a special canonical form. The necessary and sufficient conditions for the existence of the PTUIO are established in terms of the original system matrices. Finally, two examples are presented to verify the effectiveness of the proposed method.