Global stabilization of multiple integrators by a bounded feedback with constraints on its successive derivatives

Jonathan Laporte (1) , Antoine Chaillet (1) , Yacine Chitour (1)

1 L2S - Laboratoire des signaux et systèmes

In this paper, we address the global stabilization of chains of integrators by means of a bounded static feedback law whose p first time derivatives are bounded. Our construction is based on the technique of nested saturations introduced by Teel. We show that the control amplitude and the maximum value of its p first derivatives can be imposed below any prescribed values. Our results are illustrated by the stabilization of the third order integrator on the feedback and its first two derivatives.

Mots clés: integrator chains; stabilization; saturated control

Domaines: Automatique / Robotique

Jonathan Laporte, Antoine Chaillet, Yacine Chitour. Global stabilization of multiple integrators by a bounded feedback with constraints on its successive derivatives. 54th IEEE Conference on Decision and Control (CDC), Dec 2015, Osaka, Japan. ⟨10.1109/cdc.2015.7402838⟩. ⟨hal-01133844⟩