# Robust stabilization in the Martinet case

Abstract : In a previous work, we derived a result of semi-global minimal time robust stabilization for analytic control systems with controls entering linearly, by means of a hybrid state feedback law, under the main assumption of the absence of minimal time singular trajectories. In this paper, we investigate the Martinet case, which is a model case in $\R^3$ where singular minimizers appear, and show that such a stabilization result still holds. Namely, we prove that the solutions of the closed-loop system converge to the origin in quasi minimal time (for a given bound on the controller) with a robustness property with respect to small measurement noise, external disturbances and actuator errors.
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Journal articles

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https://hal.archives-ouvertes.fr/hal-00086365
Contributor : Emmanuel Trélat <>
Submitted on : Tuesday, July 18, 2006 - 6:57:39 PM
Last modification on : Friday, January 10, 2020 - 9:08:09 PM
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• HAL Id : hal-00086365, version 1

### Citation

Christophe Prieur, Emmanuel Trélat. Robust stabilization in the Martinet case. Control and Cybernetics, Polish Academy of Sciences, 2006, 35 (4), pp.923--945. ⟨hal-00086365⟩

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