{
  "id": "1006.2212",
  "version": "v1",
  "published": "2010-06-11T07:03:08.000Z",
  "updated": "2010-06-11T07:03:08.000Z",
  "title": "Boundary feedback stabilization by piecewise constant time delay for the wave equation",
  "authors": [
    "Martin Gugat",
    "Marius Tucsnak"
  ],
  "comment": "18 pages",
  "categories": [
    "math.OC",
    "math.DS"
  ],
  "abstract": "For vibrating systems, a delay in the application of a feedback control can destroy the stabilizing effect of the control. In this paper we consider a vibrating string that is fixed at one end and stabilized with a boundary feedback with delay at the other end. We show that for certain feedback parameters the system is exponentially stable with constant delays of the form 4L/c, 8L/c, 12L/c ... Moreover, we show that the system is exponentially stable with piecewise constant delays that attain the values 4L/c and 8L/c.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-06-11T07:03:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "93C20",
      "93B52"
    ],
    "keywords": [
      "piecewise constant time delay",
      "boundary feedback stabilization",
      "wave equation",
      "constant delays",
      "values 4l/c"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1006.2212G"
    }
  }
}