W-transform for exponential stability of second order delay differential equations without damping terms

Alexander Domoshnitsky; Abraham Maghakyan; Leonid Berezansky

doi:10.1186/s13660-017-1296-0

W-transform for exponential stability of second order delay differential equations without damping terms

Alexander Domoshnitsky, Abraham Maghakyan, Leonid Berezansky

Department of Mathematics

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

14 Scopus citations

Abstract

In this paper a method for studying stability of the equation x″(t)+∑i=1mai(t)x(t−τi(t))=0 not including explicitly the first derivative is proposed. We demonstrate that although the corresponding ordinary differential equation x″(t)+∑i=1mai(t)x(t)=0 is not exponentially stable, the delay equation can be exponentially stable.

Original language	English
Article number	20
Journal	Journal of Inequalities and Applications
Volume	2017
Issue number	1
DOIs	https://doi.org/10.1186/s13660-017-1296-0
State	Published - 1 Dec 2017

Keywords

W-method
exponential stability
second order delay differential equations

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

Access to Document

10.1186/s13660-017-1296-0

Cite this

@article{5d6b3d6eb9064d1283c7ee52c8c07bce,

title = "W-transform for exponential stability of second order delay differential equations without damping terms",

abstract = "In this paper a method for studying stability of the equation x″(t)+∑i=1mai(t)x(t−τi(t))=0 not including explicitly the first derivative is proposed. We demonstrate that although the corresponding ordinary differential equation x″(t)+∑i=1mai(t)x(t)=0 is not exponentially stable, the delay equation can be exponentially stable.",

keywords = "W-method, exponential stability, second order delay differential equations",

author = "Alexander Domoshnitsky and Abraham Maghakyan and Leonid Berezansky",

note = "Publisher Copyright: {\textcopyright} 2017, The Author(s).",

year = "2017",

month = dec,

day = "1",

doi = "10.1186/s13660-017-1296-0",

language = "English",

volume = "2017",

journal = "Journal of Inequalities and Applications",

issn = "1025-5834",

publisher = "Springer Nature",

number = "1",

}

TY - JOUR

T1 - W-transform for exponential stability of second order delay differential equations without damping terms

AU - Domoshnitsky, Alexander

AU - Maghakyan, Abraham

AU - Berezansky, Leonid

PY - 2017/12/1

Y1 - 2017/12/1

N2 - In this paper a method for studying stability of the equation x″(t)+∑i=1mai(t)x(t−τi(t))=0 not including explicitly the first derivative is proposed. We demonstrate that although the corresponding ordinary differential equation x″(t)+∑i=1mai(t)x(t)=0 is not exponentially stable, the delay equation can be exponentially stable.

AB - In this paper a method for studying stability of the equation x″(t)+∑i=1mai(t)x(t−τi(t))=0 not including explicitly the first derivative is proposed. We demonstrate that although the corresponding ordinary differential equation x″(t)+∑i=1mai(t)x(t)=0 is not exponentially stable, the delay equation can be exponentially stable.

KW - W-method

KW - exponential stability

KW - second order delay differential equations

UR - https://www.scopus.com/pages/publications/85009932118

U2 - 10.1186/s13660-017-1296-0

DO - 10.1186/s13660-017-1296-0

M3 - Article

AN - SCOPUS:85009932118

SN - 1025-5834

VL - 2017

JO - Journal of Inequalities and Applications

JF - Journal of Inequalities and Applications

IS - 1

M1 - 20

ER -

W-transform for exponential stability of second order delay differential equations without damping terms

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this