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

Jonathan Laporte
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Antoine Chaillet
Yacine Chitour

Abstract

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.

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hal-01133844 , version 1 (20-03-2015)

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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⟩
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