Global stabilization of linear systems with bounded controls by the energy function with applications to the spacecraft rendezvous

This paper revisits the problem of global stabilization of linear systems with bounded controls by using nested saturation functions. The energy function analysis based approach is firstly utilized to stabilize a planar linear system by using bounded linear feedback. Then, by using the Teel's canonical forms which were carefully studied in this paper, the results for planar systems were utilized to stabilize general linear systems with a single input by applying a recursive design. A systematic way for designing global stabilizing controllers for a general linear systems having multiple inputs is then proposed. The established design procedure is given in an explicit and recursive way, and thus are more easy to use than the existing one. Finally, the proposed approach is applied on the circular spacecraft rendezvous systems to design global stabilizing controllers and the effectiveness of the proposed controllers are illustrated by numerical simulations.