On prescribed-time functional observer design

In this paper, the prescribed-time functional observer (PTFO) design for a class of linear systems is considered. Differs from the traditional functional observer design, for the target vector z to be estimated, in this paper, we establish a new observable LTI system by treating the target vector z as the state, which actually transforms the functional observer design problem into a norm Luenberger observer design problem, and thus making the functional observer design more simpler and straightforward. Then, based on the new linear system with z acting as the state, a prescribed-time functional observer is constructed which provides an exact estimation of z after an arbitrarily prescribed time instant. The necessary and sufficient conditions for the existence of such the PTFO are also provided in terms of the original system matrices which are easy to examine. Finally, one numerical example is provided to illustrate the effectiveness of the proposed method.