{
  "id": "1804.08505",
  "version": "v1",
  "published": "2018-04-23T15:27:19.000Z",
  "updated": "2018-04-23T15:27:19.000Z",
  "title": "Standard versus Bounded Real Lemma with infinite-dimensional state space II: The storage function approach",
  "authors": [
    "J. A. Ball",
    "G. J. Groenewald",
    "S. ter Horst"
  ],
  "comment": "45 pages, to appear in Operator Theory: Advances and Applications volume",
  "categories": [
    "math.FA"
  ],
  "abstract": "For discrete-time causal linear input/state/output systems, the Bounded Real Lemma explains (under suitable hypotheses) the contractivity of the values of the transfer function over the unit disk for such a system in terms of the existence of a positive-definite solution of a certain Linear Matrix Inequality (the Kalman-Yakubovich-Popov (KYP) inequality). Recent work has extended this result to the setting of infinite-dimensional state space and associated non-rationality of the transfer function, where at least in some cases unbounded solutions of the generalized KYP-inequality are required. This paper is the second installment in a series of papers on the Bounded Real Lemma and the KYP inequality. We adapt Willems' storage-function approach to the infinite-dimensional linear setting, and in this way reprove various results presented in the first installment, where they were obtained as applications of infinite-dimensional State-Space-Similarity theorems, rather than via explicit computation of storage functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-23T15:27:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A63",
      "47A48",
      "93B20",
      "93C55",
      "47A56"
    ],
    "keywords": [
      "bounded real lemma",
      "infinite-dimensional state space",
      "storage function approach",
      "discrete-time causal linear input/state/output systems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}