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

[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.

[发布日期] 2021-12-15

[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