On nonoscillation and stability for systems of differential equations with a distributed delay

Leonid Berezansky; Elena Braverman

doi:10.1016/j.automatica.2011.08.062

On nonoscillation and stability for systems of differential equations with a distributed delay

Leonid Berezansky, Elena Braverman

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

For the system with a distributed delay Ẋ(t)+∑k= 1m∫ ^hk(t)t[ ^dsRk(t,s)]X(s)=0 and a nonnegative fundamental matrix, solution estimates and stability results are obtained. The results are applied to integrodifferential equations and equations of mixed type including both distributed and concentrated delays.

Original language	English
Pages (from-to)	612-618
Number of pages	7
Journal	Automatica
Volume	48
Issue number	4
DOIs	https://doi.org/10.1016/j.automatica.2011.08.062
State	Published - 1 Apr 2012

Keywords

Distributed delay
Exponential stability
Fundamental matrix
Linear systems
Nonoscillation
Solution estimation

ASJC Scopus subject areas

Control and Systems Engineering
Electrical and Electronic Engineering

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10.1016/j.automatica.2011.08.062

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title = "On nonoscillation and stability for systems of differential equations with a distributed delay",

abstract = "For the system with a distributed delay Ẋ(t)+∑k= 1m∫ hk(t)t[ dsRk(t,s)]X(s)=0 and a nonnegative fundamental matrix, solution estimates and stability results are obtained. The results are applied to integrodifferential equations and equations of mixed type including both distributed and concentrated delays.",

keywords = "Distributed delay, Exponential stability, Fundamental matrix, Linear systems, Nonoscillation, Solution estimation",

author = "Leonid Berezansky and Elena Braverman",

note = "Funding Information: The first author was partially supported by Israeli Ministry of Absorption . The second author was partially supported by NSERC . The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor George Weiss under the direction of Editor Miroslav Krstic. ",

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AU - Berezansky, Leonid

AU - Braverman, Elena

N1 - Funding Information: The first author was partially supported by Israeli Ministry of Absorption . The second author was partially supported by NSERC . The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor George Weiss under the direction of Editor Miroslav Krstic.

PY - 2012/4/1

Y1 - 2012/4/1

N2 - For the system with a distributed delay Ẋ(t)+∑k= 1m∫ hk(t)t[ dsRk(t,s)]X(s)=0 and a nonnegative fundamental matrix, solution estimates and stability results are obtained. The results are applied to integrodifferential equations and equations of mixed type including both distributed and concentrated delays.

AB - For the system with a distributed delay Ẋ(t)+∑k= 1m∫ hk(t)t[ dsRk(t,s)]X(s)=0 and a nonnegative fundamental matrix, solution estimates and stability results are obtained. The results are applied to integrodifferential equations and equations of mixed type including both distributed and concentrated delays.

KW - Distributed delay

KW - Exponential stability

KW - Fundamental matrix

KW - Linear systems

KW - Nonoscillation

KW - Solution estimation

UR - http://www.scopus.com/inward/record.url?scp=84858153698&partnerID=8YFLogxK

U2 - 10.1016/j.automatica.2011.08.062

DO - 10.1016/j.automatica.2011.08.062

M3 - Article

AN - SCOPUS:84858153698

SN - 0005-1098

VL - 48

SP - 612

EP - 618

JO - Automatica

JF - Automatica

IS - 4

ER -

On nonoscillation and stability for systems of differential equations with a distributed delay

Abstract

Keywords

ASJC Scopus subject areas

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