{
  "id": "1801.09557",
  "version": "v1",
  "published": "2018-01-29T15:07:28.000Z",
  "updated": "2018-01-29T15:07:28.000Z",
  "title": "Families of Solutions of Algebraic Riccati Equations",
  "authors": [
    "Daniele Alpago",
    "Augusto Ferrante"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "We consider Homogeneous Algebraic Riccati Equations in the general situation when the matrix of the dynamics can be \"mixed\". We show that in this case the equation may have infinitely many families of solutions. An analysis of these families is carried over and explicit formulas are derived. We also derive sufficient conditions under which the union of the families covers the whole set of solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-29T15:07:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "homogeneous algebraic riccati equations",
      "general situation",
      "explicit formulas",
      "derive sufficient conditions",
      "families covers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}