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

13 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

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10.1186/s13660-017-1296-0

Cite this

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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.",

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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.

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

Abstract

Keywords

ASJC Scopus subject areas

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