Exponential stability of linear differential-difference equations of neutral type

Balandin, A. S.; Malygina, V. V.

doi:10.3103/s1066369x0707002x

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2020

2024

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Cited by 6 publications

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“…We refer the reader to the review of known stability results for neutral equations in [3]. For a particular case of constant coefficients and delays sharp results are obtained in [2]. The recent paper [5] contains exponential estimates for solutions of delay differential equations without the neutral term (a(t) ≡ 0 in (1.7)), see also [10].…”

Section: Introductionmentioning

confidence: 99%

Solution estimates and stability tests for linear neutral differential equations

Berezansky

Braverman

2020

Applied Mathematics Letters

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Explicit exponential stability tests are obtained for the scalar neutral differential equatioṅ x(t) − a(t)ẋ(g(t)) = − m k=1 b k (t)x(h k (t)), together with exponential estimates for its solutions. Estimates for solutions of a non-homogeneous neutral equation are also obtained, they are valid on every finite segment, thus describing both asymptotic and transient behavior. For neutral differential equations, exponential estimates are obtained here for the first time. Both the coefficients and the delays are assumed to be measurable, not necessarily continuous functions.

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