{
  "id": "1006.1749",
  "version": "v3",
  "published": "2010-06-09T09:10:57.000Z",
  "updated": "2011-02-15T15:56:21.000Z",
  "title": "Converse Lyapunov Theorems for Switched Systems in Banach and Hilbert Spaces",
  "authors": [
    "Falk Hante",
    "Mario Sigalotti"
  ],
  "journal": "SIAM Journal on Control and Optimization, Vol. 49, Nr. 2, pp. 752--770, 2011",
  "doi": "10.1137/100801561",
  "categories": [
    "math.OC",
    "cs.SY"
  ],
  "abstract": "We consider switched systems on Banach and Hilbert spaces governed by strongly continuous one-parameter semigroups of linear evolution operators. We provide necessary and sufficient conditions for their global exponential stability, uniform with respect to the switching signal, in terms of the existence of a Lyapunov function common to all modes.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-02-15T15:56:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "converse lyapunov theorems",
      "hilbert spaces",
      "switched systems",
      "linear evolution operators",
      "global exponential stability"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1006.1749H"
    }
  }
}