{
  "id": "2012.11507",
  "version": "v1",
  "published": "2020-12-21T17:25:55.000Z",
  "updated": "2020-12-21T17:25:55.000Z",
  "title": "Asymptotic properties of neutral type linear systems",
  "authors": [
    "Leonid Berezansky",
    "Elena Braverman"
  ],
  "comment": "16 pages, no figures. Accepted to Journal of Mathematical Analysis and Applications",
  "categories": [
    "math.DS"
  ],
  "abstract": "Exponential stability and solution estimates are investigated for a delay system $$ \\dot{x}(t) - A(t)\\dot{x}(g(t))=\\sum_{k=1}^m B_k(t)x(h_k(t)) $$ of a neutral type, where $A$ and $B_k$ are $n\\times n$ bounded matrix functions, and $g, h_k$ are delayed arguments. Stability tests are applicable to a wide class of linear neutral systems with time-varying coefficients and delays. In addition, explicit exponential estimates for solutions of both homogeneous and non-homogeneous neutral systems are obtained for the first time. These inequalities are not just asymptotic estimates, they are valid on every finite segment and evaluate both short- and long-term behaviour of solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-21T17:25:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34K20",
      "34K40",
      "34K25",
      "34K06"
    ],
    "keywords": [
      "neutral type linear systems",
      "asymptotic properties",
      "linear neutral systems",
      "explicit exponential estimates",
      "exponential stability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}