{
  "id": "1812.05360",
  "version": "v1",
  "published": "2018-12-13T11:04:05.000Z",
  "updated": "2018-12-13T11:04:05.000Z",
  "title": "Impulse response of bilinear systems based on Volterra series representation",
  "authors": [
    "Maria Cruz Varona",
    "Raphael Gebhart"
  ],
  "comment": "34 pages, 8 figures",
  "categories": [
    "math.NA",
    "cs.SY",
    "math.DS"
  ],
  "abstract": "This paper focuses on the systems theory of bilinear dynamical systems using the Volterra series representation. The main contributions are threefold. First, we gain an input-output representation in the frequency domain, where the Laplace transform of the kernels can indeed be interpreted as transfer functions. Then, we derive the response of bilinear systems to a nascent delta function in time domain, i.e. the impulse response of bilinear systems. Finally, we study the relationships between this novel impulse response and the well-known Volterra kernels and adjust those to be compatible to the impulse response.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-13T11:04:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "93C10",
      "93C15",
      "93A15"
    ],
    "keywords": [
      "volterra series representation",
      "bilinear systems",
      "nascent delta function",
      "novel impulse response",
      "well-known volterra kernels"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}