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

ABSTRACT 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.