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Stabilization of a linear Korteweg-de Vries equation with a saturated internal control

Abstract : — This article deals with the design of saturated controls in the context of partial differential equations. It is focused on a linear Korteweg-de Vries equation, which is a mathematical model of waves on shallow water surfaces. In this article, we close the loop with a saturating input that renders the equation nonlinear. The well-posedness is proven thanks to the nonlinear semigroup theory. The proof of the asymptotic stability of the closed-loop system uses a Lyapunov function.
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https://hal.archives-ouvertes.fr/hal-01193019
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Submitted on : Friday, September 4, 2015 - 10:38:44 AM
Last modification on : Thursday, August 4, 2022 - 5:14:18 PM
Long-term archiving on: : Saturday, December 5, 2015 - 12:02:13 PM

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  • HAL Id : hal-01193019, version 1
  • ARXIV : 1509.01471

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Swann Marx, Eduardo Cerpa, Christophe Prieur, Vincent Andrieu. Stabilization of a linear Korteweg-de Vries equation with a saturated internal control. ECC 2015 - 14th European Control Conference, Jul 2015, Linz, Austria. ⟨hal-01193019⟩

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