{
  "id": "2212.12054",
  "version": "v1",
  "published": "2022-12-22T22:06:42.000Z",
  "updated": "2022-12-22T22:06:42.000Z",
  "title": "Canonical forms for polynomial systems with balanced super-linearizations",
  "authors": [
    "M. -A. Belabbas"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "A system is Koopman super-linearizable if it admits a finite-dimensional embedding as a linear system. Super-linearization is used to leverage methods from linear systems theory to design controllers or observers for nonlinear systems. We call a super-linearization balanced if the degrees of the hidden observables do not exceed the ones of the visible observables. We show that systems admitting such super-linearization can be put in a simple canonical form via a linear change of variables.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-22T22:06:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "polynomial systems",
      "balanced super-linearizations",
      "linear systems theory",
      "design controllers",
      "nonlinear systems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}