{
  "id": "2208.10829",
  "version": "v1",
  "published": "2022-08-23T09:21:19.000Z",
  "updated": "2022-08-23T09:21:19.000Z",
  "title": "Sufficient Conditions for Robust Safety in Differential Inclusions Using Barrier Functions",
  "authors": [
    "Mohamed Maghenem",
    "Masoumeh Ghanbarpour",
    "Adnane Saoud"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "In this brief paper we introduce a robust-safety notion for differential inclusions, and we propose a general framework to certify such a notion in terms of barrier functions. While existing literature studied only what we designate by uniform robust safety, in this paper, we make a clear distinction between the uniform and the non-uniform robust-safety notions. For both cases, we establish sufficient (infinitesimal) conditions on the nominal (unperturbed) system. That is, our conditions involve only the barrier function and the system's right-hand side. Our results allow for unbounded safety regions as well as nonsmooth barrier functions. Throughout the paper, simple examples are provided to illustrate our results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-23T09:21:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "differential inclusions",
      "sufficient conditions",
      "nonsmooth barrier functions",
      "non-uniform robust-safety notions",
      "systems right-hand side"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}