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

Leonid Berezansky, Elena Braverman

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

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˙i(t)=Ai(t)xi(hi(t))+∑j=1n∑k=1mijBijk(t)xj(hijk(t))+∑j=1n∫gij(t)tKij(t,s)xj(s)ds,i=1,…,n. Here xi are unknown vector-functions, Ai,Bijk,Kij are matrix functions, hi,hijk,gij are delayed arguments. Using these results, we deduce explicit exponential stability tests for second order vector delay differential equations.

Original languageEnglish
Article number125566
JournalJournal of Mathematical Analysis and Applications
Volume504
Issue number2
DOIs
StatePublished - 15 Dec 2021

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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