{
  "id": "1809.03083",
  "version": "v1",
  "published": "2018-09-10T02:04:50.000Z",
  "updated": "2018-09-10T02:04:50.000Z",
  "title": "Stabilization of regime-switching processes by feedback control based on discrete time observations II: state-dependent case",
  "authors": [
    "Jinghai Shao",
    "Fubao Xi"
  ],
  "comment": "33 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "This work investigates the almost sure stabilization of a class of regime-switching systems based on discrete-time observations of both continuous and discrete components. It develops Shao's work [SIAM J. Control Optim., 55(2017), pp. 724--740] in two aspects: first, to provide sufficient conditions for almost sure stability in lieu of moment stability; second, to investigate a class of state-dependent regime-switching processes instead of state-independent ones. To realize these developments, we establish an estimation of the exponential functional of Markov chains based on the spectral theory of linear operator. Moreover, through constructing order-preserving coupling processes based on Skorokhod's representation of jumping process, we realize the control from up and below of the evolution of state-dependent switching process by state-independent Markov chains.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-10T02:04:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "discrete time observations",
      "regime-switching processes",
      "state-dependent case",
      "feedback control",
      "state-independent markov chains"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}