Exponential stability of systems of vector delay differential equations with applications to second order equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:504

Article

Berezansky, Leonid¹  Braverman, Elena² 

[1] Ben Gurion Univ Negev, Dept Math, IL-84105 Beer Sheva, Israel

[2] Univ Calgary, Dept Math & Stats, Calgary, AB T2N 1N4, Canada

关键词: Exponential stability;    Differential systems with matrix coefficients and a distributed delay;    Second order vector delay differential equations;    Bohl-Perron theorem;    Matrix measure;    M-matrices;   

DOI  :  10.1016/j.jmaa.2021.125566

来源: Elsevier

【 摘 要 】

Various results and techniques, such as the Bohl-Perron theorem, a priori estimates of solutions, M-matrices and the matrix measure, are applied to obtain new explicit exponential stability conditions for the system of vector functional differential equations (x)over dot(i)(t) = A(i)(t)x(i)(h(i)(t)) + Sigma(n)(j=1) Sigma(n)(k=1) B-ij(k)(t)x(j)(h(ij)(k)(t)) + Sigma(n)(j=1) integral(t)(gij(t)) K-ij(t, s)x(j)(s)ds, i = 1, ..., n. Here xi 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. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free