Stability of vector functional differential equations with oscillating coefficients

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3 Scopus citations

Abstract

As it is well known, an ODE with a sufficiently quickly oscillating matrix coefficient A(t) is stable even, if A(t) is not Hurwitzian for each t ≥ 0. We prove the similar result for the equation dx(t)/dt = A(t) ∫η0 R(ds)x(t - s) (η = const > 0), where R(τ) is a matrix-valued function having a bounded variation. Besides, the function det (z + A(t) ∫η0 e-zsR(ds)) can have zeros in the open right-hand plane for some t ≥ 0. It is shown that the considered equation is exponentially stable provided A(t) = B + C(t), where B is a constant matrix satisfying some conditions and the integral ∫t0 C(s)ds is sufficiently small for all t > 0.

Original languageEnglish
Pages (from-to)26-33
Number of pages8
JournalJournal of Advanced Research in Dynamical and Control Systems
Volume3
Issue number1
StatePublished - 28 Nov 2011

Keywords

  • Exponential stability
  • Linear vector functional differential equation

ASJC Scopus subject areas

  • Computer Science (all)
  • Engineering (all)

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