Exponential stabilization of nonlinear driftless systems with robustness to unmodeled dynamics

Abstract. Exponential stabilization of nonlinear driftless ane control systems is addressed with the concern of achieving robustness with respect to imperfect knowledge of the system’s control vector elds. In order to satisfy this robustness requirement, and inspired by Bennani and Rouchon [1] where the same issue was rst addressed, we consider a control strategy which consists in applying periodically updated open-loop controls that are continuous with respect to state initial conditions. These controllers are more precisely described as continuous time-periodic feedbacks associated with a specic dynamic extension of the original system. Sucient conditions which, if they are satised by the control law, ensure that the control is a robust exponential stabilizer for the extended system are given. Explicit and simple control expressions which satisfy these conditions in the case of n-dimensional chained systems are proposed. A constructive algorithm for the design of such control laws, which applies to any (suciently regular) driftless control system, is described. Resume. Pour les systemes de commande sans derive, le probleme de la stabilisation exponentielle est considere, avec pour principal objectif l’obtention de commandes robustes par rapport aux erreurs de modelisation sur les champs de commande. Motives par Bennani et Rouchon [1], ou ce probleme de robustesse a deja ete etudie, nous considerons des lois de commande en boucle ouverte, reinitialisee