Fixed-Time Feedback Control Design of Input-Delay Spacecraft Rendezvous System Based on Fully Actuated System Theory

This paper investigates the prescribed-time feedback control design for linear elliptical orbital rendezvous systems with input delays. First, a linear transformation is employed to convert the time-delayed control problem into a delay-free linear periodic system. Then, by integrating the parameterized Lyapunov equation approach with periodic delay feedback control, a composite linear periodic delayed feedback control law is designed. Under this control law, the linear spacecraft rendezvous system achieves prescribed-time stability, where the convergence time is independent of initial conditions. The proposed method enhances the robustness and performance of spacecraft rendezvous systems in elliptical orbits. Numerical simulations are provided to validate the effectiveness of the control methodology, demonstrating its potential for practical space mission applications.