Attitude stabilization of a rigid spacecraft based on MRPs with unknown bounded time-delay

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.