{
  "annotation_id": "01bbe212-dc1c-47d0-8a16-ecab2751ab1d",
  "date_created": "2026-02-17T05:53:12.550000Z",
  "date_modified": "2026-02-17T05:53:12.550000Z",
  "file_hash": "e14b03907d087dccd6edef5307f43e25118701897978605ba32d3538b7c6d2ea",
  "private": false,
  "record": {
    "abstract": "We establish sufficient conditions for positive (semi-)definiteness, with or without radial unboundedness, for nonquadratic Lyapunov function constructed as sign-indefinite quadratic forms involving the state and the deadzone of a suitable input. We then use these conditions to build weak nonquadratic Lyapunov functions establishing global asymptotic stability of linear systems in feedback through a saturation, leveraging invariance principles. Our results are shown to be non-conservative (necessary and sufficient) for a family of well known prototypical examples of linear SISO feedbacks that are not globally exponentially stabilizable (the so-called ANCBI plants). Our multi-input extension leads to convex stability analysis tests, formulated as linear matrix inequalities that are applicable to ANCBI non-globally-exponentially-stabilizable plants.",
    "arxiv_id": "2601.07431",
    "authors": [
      "Andrea Cristofaro",
      "Luca Zaccarian"
    ],
    "categories": [
      "math.OC",
      "cs.SY",
      "eess.SY"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "title": "Nonquadratic global asymptotic stability certificates for saturated linear feedbacks",
    "url": "https://arxiv.org/abs/2601.07431",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "204b018b-1395-4ec9-ba56-f5e14dd63a99",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}