Exponential stabilization of the attitude of a rigid spacecraft with two controls

Rigid spacecraft models with two controls can not be locally asymptotically stabilized by continuous pure-state feedbacks. The existing smooth time-varying control results suffer from the drawback that the designed control laws do not stabilize the system with exponential convergence rate. The existing control laws which can exponentially stabilizing the system are nonsmooth. In this paper, by introducing an assistant state variable and using the feedback linearization technique, smooth time-varying controllers are developed. Besides the advantage of design simplicity, the states of the closed loop system converge with exponential rate. The simulation results are provided to show the effectiveness of our method.