{
  "id": "2104.00928",
  "version": "v1",
  "published": "2021-04-02T08:11:47.000Z",
  "updated": "2021-04-02T08:11:47.000Z",
  "title": "Serial interconnections of 1-contracting and 2-contracting systems",
  "authors": [
    "Ron Ofir",
    "Michael Margaliot",
    "Yoash Levron",
    "Jean-Jacques Slotine"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "The flow of contracting systems contracts 1-dimensional polygons (i.e. lines) at an exponential rate. One reason for the usefulness of contracting systems is that many interconnections of contracting sub-systems yield an overall contracting system. A recent generalization of contracting systems is called $k$-contracting systems, where $k\\in\\{1,\\dots,n\\}$. The flow of such systems contracts $k$-dimensional polygons at an exponential rate, and in particular they reduce to contracting systems when $k=1$. Here, we analyze serial interconnections of $1$-contracting and $2$-contracting systems. We provide conditions guaranteeing that such interconnections have a well-ordered asymptotic behaviour, and demonstrate the theoretical results using several examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-02T08:11:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "exponential rate",
      "analyze serial interconnections",
      "contracting systems contracts",
      "overall contracting system",
      "dimensional polygons"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}