A prescribed-time functional observer for systems with unknown input

This paper different from traditional approaches, proposes a novel method where the target vector z is treated as the state variable of an observer LTI system by system reformulations, which greatly facilitates the use of the classical Luenberger state observer to address the prescribed-time functional observer (PTFO) design issue. Subsequently, for the newly formulated LTI system with z as the state variable, a PTFO is developed for the single-output case that is capable of accurately estimating z within a user-defined time, and is subsequently extended to the multiple-output case. More importantly, it can avoid the jumps that usually occur in Engel's prescribed-time observers. Besides, The sufficient and necessary conditions for PTFO realization are explicitly formulated through the original system matrices, thereby enabling designers/users to conduct preliminary compatibility assessments prior to control scheme implementation. Finally, two examples are presented to demonstrate the effectiveness of the proposed method.