Time-varying exponential stabilization of the attitude of a rigid spacecraft with two controls

Rigid body models with two controls cannot be locally asymptotically stabilized by continuous feedback which are functions of the state only. However, explicit smooth time-varying feedback which locally asymptotically stabilize the attitude of a rigid spacecraft have previously been proposed by the authors (1995). Due to the smoothness of the control law, the stabilization is not exponential and the asymptotical convergence rate to the desired equilibrium is only polynomial in the worst case. Nevertheless, exponential convergence can be obtained by considering time-varying feedback which are only continuous at the equilibrium. This paper proposes explicit feedback control laws of this type.