Exponential stability for systems of delay differential equations with block matrices

Leonid Berezansky, Elena Braverman

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We obtain efficient exponential stability tests for a system ẋ(t)=A(t)x(h(t)), where A is a block matrix and h(t) is a delay function, in terms of norms and matrix measures of blocks. Compared to the analysis of the whole matrix A, handling blocks can be more manageable even for the system ẋ(t)=A(t)x(t) without delay. In a presented example, the criterion applied to A fails, while considering appropriate blocks leads to exponential stability. Another example illustrates efficiency even in the case of a non-delay system.

Original languageEnglish
Article number107364
JournalApplied Mathematics Letters
Volume121
DOIs
StatePublished - 1 Nov 2021

Keywords

  • A block matrix
  • A spectral radius
  • Bohl–Perron theorem
  • Differential systems with delay
  • Exponential stability
  • Matrix measure

ASJC Scopus subject areas

  • Applied Mathematics

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