Analytical solutions to the matrix inequalities in the ILF control-observer scheme for non-cooperative rendezvous with unknown inertia parameters

In this paper, the problem of robust control for non-cooperative rendezvous is investigated based on implicit Lyapunov function (ILF) method. The dynamical model of relative motion between two spacecrafts is established in the body coordinate system of the chaser spacecraft without using the target-orbital information. In view of unknown inertia parameters and external disturbances, an ILF control-observer scheme is introduced, where the ideal controller is first designed and then estimated by the observer. The closed-loop system is proved to be finite-time stable, and the controller and observer gains are, respectively, obtained by solving linear matrix inequalities and parameterised nonlinear matrix inequalities. To reduce the computational burden, analytical solutions to these matrix inequalities are provided. The effectiveness of the theoretical results is demonstrated by simulation examples.