Explicit stability tests for linear neutral delay equations using infinite series

Leonid Berezansky, Elena Braverman

Research output: Contribution to journalArticlepeer-review


We obtain new, explicit exponential stability conditions for the linear scalar neutral equation with two bounded delays (x(t) − a(t)x(g(t)))0 + b(t)x(h(t)) = 0, where |a(t)| ≤ A0 < 1, 0 < b0 ≤ b(t) ≤ B0, assuming that all parameters of the equation are measurable functions. To analyze the exponential stability, we apply the Bohl-Perron theorem and a reduction of a neutral equation to an equation with an infinite number of non-neutral delay terms. This method has never before been used for this neutral equation; its application allows omitting a usual restriction |a(t)| < 1/2 in known asymptotic stability tests and the consideration of variable delays.

Original languageEnglish
Pages (from-to)387-403
Number of pages17
JournalRocky Mountain Journal of Mathematics
Issue number2
StatePublished - 1 Jan 2019


  • Bohl-perron theorem
  • Explicit stability conditions
  • Neutral equations in hale form
  • Uniform exponential stability
  • Variable delays

ASJC Scopus subject areas

  • Mathematics (all)


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