Exponential stability of linear delayed differential systems

Leonid Berezansky; Josef Diblík; Zdeněk Svoboda; Zdeněk Šmarda

doi:10.1016/j.amc.2017.10.013

Exponential stability of linear delayed differential systems

Leonid Berezansky, Josef Diblík, Zdeněk Svoboda, Zdeněk Šmarda

Department of Mathematics

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

8 Scopus citations

Abstract

Linear delayed differential systems x˙_i(t)=−∑j=1m∑k=1r_ija_ij^k(t)x_j(h_ij^k(t)),i=1,…,mare analyzed on a half-infinity interval t ≥ 0. It is assumed that m and r_ij, i,j=1,…,m are natural numbers and the coefficients a_ij^k:[0,∞)→R and delays h_ij^k:[0,∞)→R are measurable functions. New explicit results on uniform exponential stability are derived including, as partial cases, recently published results.

Original language	English
Pages (from-to)	474-484
Number of pages	11
Journal	Applied Mathematics and Computation
Volume	320
DOIs	https://doi.org/10.1016/j.amc.2017.10.013
State	Published - 1 Mar 2018

Keywords

Bohl–Perron theorem
Exponential stability
Linear delayed differential system

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.amc.2017.10.013

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@article{d58be893d3504e048909d35341d6ab47,

title = "Exponential stability of linear delayed differential systems",

abstract = "Linear delayed differential systems x˙i(t)=−∑j=1m∑k=1rijaijk(t)xj(hijk(t)),i=1,…,mare analyzed on a half-infinity interval t ≥ 0. It is assumed that m and rij, i,j=1,…,m are natural numbers and the coefficients aijk:[0,∞)→R and delays hijk:[0,∞)→R are measurable functions. New explicit results on uniform exponential stability are derived including, as partial cases, recently published results.",

keywords = "Bohl–Perron theorem, Exponential stability, Linear delayed differential system",

author = "Leonid Berezansky and Josef Dibl{\'i}k and Zden{\v e}k Svoboda and Zden{\v e}k {\v S}marda",

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier Inc.",

year = "2018",

month = mar,

day = "1",

doi = "10.1016/j.amc.2017.10.013",

language = "English",

volume = "320",

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journal = "Applied Mathematics and Computation",

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T1 - Exponential stability of linear delayed differential systems

AU - Berezansky, Leonid

AU - Diblík, Josef

AU - Svoboda, Zdeněk

AU - Šmarda, Zdeněk

PY - 2018/3/1

Y1 - 2018/3/1

N2 - Linear delayed differential systems x˙i(t)=−∑j=1m∑k=1rijaijk(t)xj(hijk(t)),i=1,…,mare analyzed on a half-infinity interval t ≥ 0. It is assumed that m and rij, i,j=1,…,m are natural numbers and the coefficients aijk:[0,∞)→R and delays hijk:[0,∞)→R are measurable functions. New explicit results on uniform exponential stability are derived including, as partial cases, recently published results.

AB - Linear delayed differential systems x˙i(t)=−∑j=1m∑k=1rijaijk(t)xj(hijk(t)),i=1,…,mare analyzed on a half-infinity interval t ≥ 0. It is assumed that m and rij, i,j=1,…,m are natural numbers and the coefficients aijk:[0,∞)→R and delays hijk:[0,∞)→R are measurable functions. New explicit results on uniform exponential stability are derived including, as partial cases, recently published results.

KW - Bohl–Perron theorem

KW - Exponential stability

KW - Linear delayed differential system

UR - http://www.scopus.com/inward/record.url?scp=85032273653&partnerID=8YFLogxK

U2 - 10.1016/j.amc.2017.10.013

DO - 10.1016/j.amc.2017.10.013

M3 - Article

AN - SCOPUS:85032273653

SN - 0096-3003

VL - 320

SP - 474

EP - 484

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -

Exponential stability of linear delayed differential systems

Abstract

Keywords

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