Time-varying Exponential Stabilization of the Attitude of a Rigid Spacecraft with Two Controls 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 feedbacks which are functions of the state only. However, this impossibility does no longer hold when the feedback is also a function of time, and explicit smooth time-varying feedbacks which locally asymptotically stabilize the attitude of a rigid spacecraft have previously been proposed by the authors and colleagues 10]. 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 feedbacks which are only continuous at the equilibrium. The present article proposes explicit feedback control laws of this type. Stabilisation Exponentielle Instationnaire d'un Satellite avec Deux Commandes R esum e : L'orientation d'un corps rigide auquel sont appliqu ees deux commandes ne peut ^ etre stabilis ee par retour d' etat continu fonction seulement de l' etat. La sta-bilisation par retour d' etat continu d ependant egalement du temps reste cependant possible, et de tels retours d' etat, innniment dii erentiables et localement asympto-tiquement stabilisants, ont et e propos es par les auteurs et leurs coll egues dans 10]. En raison de la r egularit e de ces lois de commande, le taux de convergence asymp-totique vers l' equilibre d esir e est, dans le plus mauvais cas, seulement polyn^ omial. Toutefois, une convergence exponentielle peut ^ etre obtenue en consid erant des re-tours d' etat instationnaires seulement continus. De tels retours d' etat sont propos es dans le pr esent rapport.