An observer-based periodic delayed feedback for fixed-time stabilization of input-delay systems

A family of observer-based periodic delayed feedback (PDF) controllers are proposed in this paper for the fixed-time stabilization of the linear input-delay system with immeasurable states. By switching the controller gain to different values periodically, an explicit relationship is established between the control gain and the system matrix. To address the open-loop problem faced by the standard PDF controller, two different observer-predictor-based PDF are proposed. Both controllers ensure that the closed-loop system converges asymptotically throughout the control period. Furthermore, a modified PDF is proposed for multi-input-multi-output systems utilizing the characteristic of controllability index set and observability index set. The modified PDF can be used for the reduction of switches required in the stabilization. A simulation example on the spacecraft rendezvous is proposed to illustrate the theory of the method proposed.