{
  "id": "1809.08742",
  "version": "v1",
  "published": "2018-09-24T03:45:39.000Z",
  "updated": "2018-09-24T03:45:39.000Z",
  "title": "Unified Necessary and Sufficient Conditions for the Robust Stability of Interconnected Sector-Bounded Systems",
  "authors": [
    "Saman Cyrus",
    "Laurent Lessard"
  ],
  "categories": [
    "math.OC",
    "cs.SY"
  ],
  "abstract": "Classical conditions for ensuring the robust stability of a linear system in feedback with a sector-bounded nonlinearity include the circle, small gain, passivity, and conicity theorems. In this work, we present a similar stability condition, but expressed in terms of operators on a semi-inner product space. This increased generality leads to a clean result that can be specialized in a variety of ways. First, we show how to recover both sufficient and necessary-and-sufficient versions of the aforementioned classical results. Second, we show that suitably choosing the semi-inner product space leads to a new necessary and sufficient condition for exponential stability with a given convergence rate. Finally, in the spirit of classical robust stability analysis, we provide linear matrix inequalities that allow for the efficient verification of the conditions of our theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-24T03:45:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sufficient condition",
      "interconnected sector-bounded systems",
      "unified necessary",
      "semi-inner product space",
      "similar stability condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}