{
  "id": "0811.0061",
  "version": "v1",
  "published": "2008-11-01T05:56:12.000Z",
  "updated": "2008-11-01T05:56:12.000Z",
  "title": "Feedback Stabilization Methods for the Numerical Solution of Systems of Ordinary Differential Equations",
  "authors": [
    "Iasson Karafyllis",
    "Lars Grune"
  ],
  "comment": "33 pages, 9 figures. Submitted for possible publication to BIT Numerical Mathematics",
  "categories": [
    "math.NA",
    "math.OC"
  ],
  "abstract": "In this work we study the problem of step size selection for numerical schemes, which guarantees that the numerical solution presents the same qualitative behavior as the original system of ordinary differential equations, by means of tools from nonlinear control theory. Lyapunov-based and Small-Gain feedback stabilization methods are exploited and numerous illustrating applications are presented for systems with a globally asymptotically stable equilibrium point. The obtained results can be used for the control of the global discretization error as well.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-11-01T05:56:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42.65.-k",
      "02.60.-x",
      "02.30.Hq"
    ],
    "keywords": [
      "ordinary differential equations",
      "numerical solution",
      "asymptotically stable equilibrium point",
      "small-gain feedback stabilization methods",
      "nonlinear control theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009AIPC.1168..152K"
    }
  }
}