Exact Prescribed-Time Stabilization of Linear Systems With Amplitude and Rate Saturations by Time-varying Feedback With Applications to Spacecraft Rendezvous

This paper addresses the problem of exact prescribed-time stabilization of linear systems subject to simultaneous magnitude and rate constraints in actuators. It is worth emphasizing that, unlike conventional prescribed-time control approaches that only ensure convergence no later than a user-defined time, the exact prescribed-time control framework imposes a more stringent requirement: the closed-loop system converges precisely at the prescribed time. To satisfy this more stringent requirement under both actuator magnitude and rate constraints, a bounded linear time-varying feedback is proposed by employing the solutions to the parametric Lyapunov equations (PLEs) and combining time-varying Lyapunov-like functions. Both state feedback and observer-based output feedback are considered. The effectiveness of the presented method for a spacecraft rendezvous system is demonstrated.