Exponential stability for a system of second and first order delay differential equations

Leonid Berezansky; Elena Braverman

doi:10.1016/j.aml.2022.108127

Exponential stability for a system of second and first order delay differential equations

Leonid Berezansky, Elena Braverman

Department of Mathematics

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

2 Scopus citations

Abstract

Exponential stability of the second order linear delay differential equation in x and u-control ẍ(t)+a₁(t)ẋ(h₁(t))+a₂(t)x(h₂(t))+a₃(t)u(h₃(t))=0is studied, where indirect feedback control u̇(t)+b₁(t)u(g₁(t))+b₂(t)x(g₂(t))=0 connects u with the solution. Explicit sufficient conditions guarantee that both x and u decay exponentially.

Original language	English
Article number	108127
Journal	Applied Mathematics Letters
Volume	132
DOIs	https://doi.org/10.1016/j.aml.2022.108127
State	Published - 1 Oct 2022

Keywords

A priori estimates
Bohl–Perron theorem
Exponential stability
Linear delayed differential system
Second order delay differential equation

ASJC Scopus subject areas

Applied Mathematics

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10.1016/j.aml.2022.108127

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title = "Exponential stability for a system of second and first order delay differential equations",

abstract = "Exponential stability of the second order linear delay differential equation in x and u-control ẍ(t)+a1(t)ẋ(h1(t))+a2(t)x(h2(t))+a3(t)u(h3(t))=0is studied, where indirect feedback control {\.u}(t)+b1(t)u(g1(t))+b2(t)x(g2(t))=0 connects u with the solution. Explicit sufficient conditions guarantee that both x and u decay exponentially.",

keywords = "A priori estimates, Bohl–Perron theorem, Exponential stability, Linear delayed differential system, Second order delay differential equation",

author = "Leonid Berezansky and Elena Braverman",

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doi = "10.1016/j.aml.2022.108127",

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T1 - Exponential stability for a system of second and first order delay differential equations

AU - Berezansky, Leonid

AU - Braverman, Elena

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N2 - Exponential stability of the second order linear delay differential equation in x and u-control ẍ(t)+a1(t)ẋ(h1(t))+a2(t)x(h2(t))+a3(t)u(h3(t))=0is studied, where indirect feedback control u̇(t)+b1(t)u(g1(t))+b2(t)x(g2(t))=0 connects u with the solution. Explicit sufficient conditions guarantee that both x and u decay exponentially.

AB - Exponential stability of the second order linear delay differential equation in x and u-control ẍ(t)+a1(t)ẋ(h1(t))+a2(t)x(h2(t))+a3(t)u(h3(t))=0is studied, where indirect feedback control u̇(t)+b1(t)u(g1(t))+b2(t)x(g2(t))=0 connects u with the solution. Explicit sufficient conditions guarantee that both x and u decay exponentially.

KW - A priori estimates

KW - Bohl–Perron theorem

KW - Exponential stability

KW - Linear delayed differential system

KW - Second order delay differential equation

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DO - 10.1016/j.aml.2022.108127

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VL - 132

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

M1 - 108127

ER -

Exponential stability for a system of second and first order delay differential equations

Abstract

Keywords

ASJC Scopus subject areas

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