{
  "id": "2101.04732",
  "version": "v1",
  "published": "2021-01-12T20:05:49.000Z",
  "updated": "2021-01-12T20:05:49.000Z",
  "title": "Exponential stability of systems of vector delay differential equations with applications to second order equations",
  "authors": [
    "Leonid Berezansky",
    "Elena Braverman"
  ],
  "comment": "14 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "Various results and techniques, such as Bohl-Perron theorem, a priori solution estimates, M-matrices and the matrix measure, are applied to obtain new explicit exponential stability conditions for the system of vector functional differential equations $$ \\dot{x_i}(t)=A_i(t)x_i(h_i(t)) +\\sum_{j=1}^n \\sum_{k=1}^{m_{ij}} B_{ij}^k(t)x_j(h_{ij}^k(t)) + \\sum_{j=1}^n\\int\\limits_{g_{ij}(t)}^t K_{ij}(t,s)x_j(s)ds,~i=1,\\dots,n. $$ Here $x_i$ are unknown vector functions, $A_i, B_{ij}^k, K_{ij}$ are matrix functions, $h_i,h_{ij}^k, g_{ij}$ are delayed arguments. Using these results, we deduce explicit exponential stability tests for second order vector delay differential equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-12T20:05:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34K20",
      "34K06",
      "34K25"
    ],
    "keywords": [
      "second order equations",
      "explicit exponential stability tests",
      "order vector delay differential equations",
      "second order vector delay differential"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}