{
  "id": "math/0606430",
  "version": "v1",
  "published": "2006-06-18T16:41:18.000Z",
  "updated": "2006-06-18T16:41:18.000Z",
  "title": "Empirical balanced truncation of nonlinear systems",
  "authors": [
    "Marissa Condon",
    "Rossen I. Ivanov"
  ],
  "comment": "LaTeX, 11 pages, 2 figures",
  "journal": "Journal of Nonlinear Science, vol. 14 (2004) pp. 405-414",
  "doi": "10.1007/s00332-004-0617-5",
  "categories": [
    "math.OC",
    "math.DS"
  ],
  "abstract": "Novel constructions of empirical controllability and observability gramians for nonlinear systems for subsequent use in a balanced truncation style of model reduction are proposed. The new gramians are based on a generalisation of the fundamental solution for a Linear Time-Varying system. Relationships between the given gramians for nonlinear systems and the standard gramians for both Linear Time-Invariant and Linear Time-Varying systems are established as well as relationships to prior constructions proposed for empirical gramians. Application of the new gramians is illustrated through a sample test-system.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-06-18T16:41:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "93B05",
      "93B07",
      "93B15",
      "93B40"
    ],
    "keywords": [
      "nonlinear systems",
      "empirical balanced truncation",
      "linear time-varying system",
      "novel constructions",
      "fundamental solution"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}