Fundamental solution and asymptotic stability of linear delay differential equations

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28 Citations (Scopus)

Abstract

In this paper we formulate sufficient conditions for the asymptotic stability of linear delay systems of the form ẋ k(t)=- ∑ ℓ=0 mj=1 n a kj (ℓ)x j(t-τ kj (ℓ)) k=1,...,n t≥ 0, where a kj (0), a kj (ℓ) ∈ ℝ, τ kj (0) = 0 τ kj (ℓ) ≥ 0, k, j = 1,..., n, ℓ = 1, ..., m. In order to apply our results, we give estimates for the integral ∫ 0 |ν(t)|dt, where ν is the fundamental solution of certain associated scalar linear delay differential equations with multiple delays.

Original languageEnglish
Pages (from-to)261-287
Number of pages27
JournalDynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis
Volume13
Issue number2
Publication statusPublished - Apr 1 2006

Keywords

  • Asymptotic stability
  • Fundamental solution
  • Linear delay differential equations

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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