{
  "id": "1609.01447",
  "version": "v1",
  "published": "2016-09-06T09:13:03.000Z",
  "updated": "2016-09-06T09:13:03.000Z",
  "title": "Global stabilization of a Korteweg-de Vries equation with a distributed control saturated in L 2 -norm",
  "authors": [
    "Swann Marx",
    "Eduardo Cerpa",
    "Christophe Prieur",
    "Vincent Andrieu"
  ],
  "journal": "10th IFAC Symposium for Nonlinear Control, Aug 2016, Monterey, California, United States",
  "categories": [
    "math.AP"
  ],
  "abstract": "This article deals with the design of saturated controls in the context of partial differential equations. It is focused on a Korteweg-de Vries equation, which is a nonlinear mathematical model of waves on shallow water surfaces. The aim of this article is to study the influence of a saturating in L 2-norm distributed control on the well-posedness and the stability of this equation. The well-posedness is proven applying a Banach fixed point theorem. The proof of the asymptotic stability of the closed-loop system is tackled with a Lyapunov function together with a sector condition describing the saturating input. Some numerical simulations illustrate the stability of the closed-loop nonlinear partial differential equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-06T09:13:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "korteweg-de vries equation",
      "distributed control",
      "global stabilization",
      "closed-loop nonlinear partial differential equation",
      "shallow water surfaces"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}