In this paper, we consider the attitude stabilization of a rigid spacecraft at the presence of unknown bounded time delay. The nonlinear kinematic equation is modelled with Modified Rodrigues Parameters (MRPs) since they are nonsingular for all possible rotations and also lead to no time delay in the nonlinear term. A simple state feedback controller is designed with the control gain matrix given by Lyapunov-Krasovskii functional, which is further transformed into linear matrix inequality according to Schur complement lemma, stability is achieved. The upper boundary for the Lipschitz parameter is studied. Simulation is performed with computed Lipschitz constant and bounded time delay to verify the effectiveness of the proposed controller.

An adaptive sliding mode controller that take the advantage of adaptive control method and sliding mode control method is designed for rigid spacecraft with external bounded disturbances. By using adaptive control law, the external disturbances can be estimated which can thus improve the robustness of the control system. System vibration is eliminated by substituting the signal function with hyperbolic tangent function. The designed controller is applied in spacecraft attitude stabilization system, and we analysis the asymptotic stability of the close loop system by employing Lyapunov stability theory. The simulation results show that this method has a good robustness to external disturbances. High precision attitude stabilization control is achieved.