{
  "id": "1010.2241",
  "version": "v1",
  "published": "2010-10-11T21:13:01.000Z",
  "updated": "2010-10-11T21:13:01.000Z",
  "title": "Transverse Dynamics and Regions of Stability for Nonlinear Hybrid Limit Cycles",
  "authors": [
    "Ian R. Manchester"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "This paper presents an algorithm for computing inner estimates of the regions of attraction of limit cycles of a nonlinear hybrid system. The basic procedure is: (1) compute the dynamics of the system transverse to the limit cycle; (2) from the linearization of the transverse dynamics construct a quadratic candidate Lyapunov function; (3) search for a new Lyapunov function verifying maximal regions of orbital stability via iterated of sum-of-squares programs. The construction of the transverse dynamics is novel, and valid for a broad class of nonlinear hybrid systems. The problem of stabilization of unstable limit cycles will also be addressed, and a solution given based on stabilization of the transverse linearization.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-10-11T21:13:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonlinear hybrid limit cycles",
      "transverse dynamics",
      "nonlinear hybrid system",
      "lyapunov function verifying maximal regions",
      "quadratic candidate lyapunov function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1010.2241M"
    }
  }
}