Prescribed-time output regulation of linear systems by functional and dual observer based periodic delayed feedback

This paper studies the prescribed-time output regulation problem of linear systems. Based on the periodic delayed feedback, a functional observer (with reduced-order observer as a special case) and a dual observer based periodic controller are designed. Such smooth periodic controllers achieve prescribed-time convergence of the output regulation error to zero rather than asymptotic convergence. Compared with the full-order observer based periodic delayed feedback, the functional reduced-order and dual observer based periodic delayed feedback have lower dimensions and smaller computational costs. Compared with the functional reduced-order observer based periodic controller, the dual observer based periodic controller has a smaller dimension when the system input dimension exceeds the output dimension. In contrast, the functional reduced-order observer based periodic controller has lower dimension. The effectiveness of the established method is verified by numerical examples.