Simple uniform exponential stability conditions for a system of linear delay differential equations

Leonid Berezansky, Josef Diblík, Zdeněk Svoboda, Zdeněk Šmarda

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

Uniform exponential stability of linear systems with time varying coefficients xi(t)=-Σj=1mΣk=1rijaijk(t)xj(hijk(t)),i=1,...,mis studied, where t≥0,m and rij,i,j=1,...,m are natural numbers, aijk:[0,∞)→R and hijk:[0,∞)→R are measurable functions. New explicit result is derived with the proof based on Bohl-Perron theorem. The resulting criterion has advantages over some previous ones in that, e.g., it involves no M-matrix to establish stability. Several useful and easily verifiable corollaries are deduced and examples are provided to demonstrate the advantage of the stability result over known results.

Original languageEnglish
Pages (from-to)605-614
Number of pages10
JournalApplied Mathematics and Computation
Volume250
DOIs
StatePublished - 1 Jan 2015

Keywords

  • Bohl-Perron theorem
  • Linear delay differential system
  • Uniform exponential stability

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