A Globally Stabilizing Time-switching Control Strategy for an Underactuated Rigid Body

The paper deals with the global stabilization of the attitude of an underactuated rigid body. First a time-driven switching control law which ensures global asymptotic stability in the ideal assumption that the angular rates may perform instantaneous changes is proposed. Subsequently, we take into account the equations describing the dynamics of the angular rates and the result obtained in the ideal case is exploited to achieve asymptotic stability of the complete system. In particular, a sufficient condition to globally asymptotically stabilize the zero equilibrium of both the attitude and the angular rates is presented. Finally, some simulations results show the effectiveness of the proposed methodology.