{
  "id": "1804.08507",
  "version": "v1",
  "published": "2018-04-23T15:28:08.000Z",
  "updated": "2018-04-23T15:28:08.000Z",
  "title": "Standard versus Strict Bounded Real Lemma with infinite-dimensional state space I: The State-Space-Similarity Approach",
  "authors": [
    "J. A. Ball",
    "G. J. Groenewald",
    "S. ter Horst"
  ],
  "comment": "25 pages, to appear in Journal of Operator Theory",
  "categories": [
    "math.FA"
  ],
  "abstract": "The Bounded Real Lemma, i.e., the state-space linear matrix inequality characterization (referred to as Kalman-Yakubovich-Popov or KYP inequality) of when an input/state/output linear system satisfies a dissipation inequality, has recently been studied for infinite-dimensional discrete-time systems in a number of different settings: with or without stability assumptions, with or without controllability/observability assumptions, with or without strict inequalities. In these various settings, sometimes unbounded solutions of the KYP inequality are required while in other instances bounded solutions suffice. In a series of reports we show how these diverse results can be reconciled and unified. This first instalment focusses on the state-space-similarity approach to the bounded real lemma. We shall show how these results can be seen as corollaries of a new State-Space-Similarity theorem for infinite-dimensional linear systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-23T15:28:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A63",
      "47A48",
      "93B20",
      "93C55",
      "47A56"
    ],
    "keywords": [
      "strict bounded real lemma",
      "infinite-dimensional state space",
      "state-space-similarity approach",
      "state-space linear matrix inequality characterization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}