Prescribed-Time Unknown Input Observers Design by Using Periodic Delayed Output With Application to Fault Estimation

This article considers the design of prescribed-time unknown input observers (PTUIOs) for linear systems, i.e., observers that estimate the state of a linear system with unknown inputs at a prescribed finite time. To this end, the generalized inverse is used first to transform a form amenable for observer design. Then, PTUIOs are designed by using the periodic delayed output so that their estimation errors converge to zero at a prescribed time. Both full-order and reduced-order PTUIOs are considered. For the reduced-order observer design, an alternative approach is also adopted, based on a transformation to a generalization of the normal form. In addition, the proposed PTUIOs are applied to estimate faults. Finally, two examples are given to illustrate the effectiveness of the proposed approaches.