Functional and dual observer based prescribed-time control of linear systems by periodic delayed feedback

In this paper the prescribed-time output feedback stabilization of linear systems is addressed using both a functional observer, which includes the reduced-order observer as a special case, and a dual observer. The approach is built upon smooth periodic delayed feedback which is a special case of linear periodic time-varying feedback. In contrast to existing periodic control approaches, the proposed feedback achieves prescribed-time convergence of the state to zero rather than asymptotic convergence. At the same time its synthesis requires solving algebraic equations rather than periodic differential equations. Compared with full-order observer based output feedback, the dimensions of the dynamic equations in the reduced-order observer and dual observer based output feedback are respectively n−p and n−m, where n,m and p are respectively the number of state variables, inputs and outputs, which indicates that the established controllers are less expensive than the full-order observer based controllers in implementations. A numerical example is given to verify the effectiveness of the proposed methods.