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arXiv · 1509.01471

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

Swann Marx·Eduardo Cerpa·Christophe Prieur·Vincent Andrieu
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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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Swann Marx, Eduardo Cerpa, Christophe Prieur, Vincent Andrieu. 2015-09-04. Stabilization of a linear Korteweg-de Vries equation with a saturated internal control. https://arxiv.org/abs/1509.01471

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