Finite-time output regulation of linear systems by reduced-order and dual observer based bounded time-varying output feedback control

This paper studies the finite-time output regulation problem of linear systems. By utilising some key properties of the (dual) parametric Lyapunov equation and regulator equations, we design reduced-order and dual observer based bounded time-varying output feedback, wherein the explicit time-varying parameters are designed offline. Such controllers can successfully achieve the (prescribed) finite-time linear output regulation for any initial condition within the ellipsoid. Compared with the full-order observer based controller, the reduced-order and dual observer based time-varying controller proposed in this paper have smaller dimensions and lower computing costs. From a controller implementation perspective, compared with reduced-order observer based controller, the dual observer based controller has smaller dimensions when the system has more input dimensions than output dimensions. In contrast, the reduced-order observer based controller has lower dimensions. The effectiveness of the established methods is validated by numerical examples.