{
  "id": "2109.04126",
  "version": "v1",
  "published": "2021-09-09T09:24:48.000Z",
  "updated": "2021-09-09T09:24:48.000Z",
  "title": "Converse Lyapunov theorems for control systems with unbounded controls",
  "authors": [
    "Anna Chiara Lai",
    "Monica Motta"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "In this paper, we extend well-known relationships between global asymptotic controllability, sample stabilizability, and the existence of a control Lyapunov function to a wide class of control systems with unbounded controls, which includes control-polynomial systems. In particular, we consider open loop controls and discontinuous stabilizing feedbacks, which may be unbounded approaching the target, so that the corresponding trajectories may present a chattering behavior. A key point of our results is to prove that global asymptotic controllability, sample stabilizability, and existence of a control Lyapunov function for these systems or for an {\\em impulsive extension} of them are equivalent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-09T09:24:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "93B05",
      "93D15",
      "93D20",
      "93C10",
      "93C27"
    ],
    "keywords": [
      "converse lyapunov theorems",
      "control systems",
      "unbounded controls",
      "global asymptotic controllability",
      "control lyapunov function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}