Exponential Stability Tests for Linear Delayed Differential Systems Depending on All Delays

Leonid Berezansky, Josef Diblík, Zdeněk Svoboda, Zdeněk Šmarda

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

Linear delayed differential systems x˙i(t)=∑j=1m∑k=1rijaijk(t)xj(hijk(t)),i=1,⋯,mare considered on a half-infinity interval t≥ 0. It is assumed that m and rij, i, j= 1 , ⋯ , m are natural numbers and the coefficients aijk:[0,∞)→R and delays hijk:[0,∞)→R are Lebesgue measurable functions. New explicit results on uniform exponential stability, depending on all delays, are derived. The conditions obtained do not require the dominance of diagonal terms over the off-diagonal terms as most of the existing stability tests for non-autonomous delay differential systems do.

Original languageEnglish
Pages (from-to)2095-2108
Number of pages14
JournalJournal of Dynamics and Differential Equations
Volume31
Issue number4
DOIs
StatePublished - 1 Dec 2019

Keywords

  • Conditions depending on all delays
  • Exponential stability
  • Linear delayed differential system
  • Matrix measure

ASJC Scopus subject areas

  • Analysis

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