TY - JOUR
T1 - Exponential Stability Tests for Linear Delayed Differential Systems Depending on All Delays
AU - Berezansky, Leonid
AU - Diblík, Josef
AU - Svoboda, Zdeněk
AU - Šmarda, Zdeněk
N1 - Funding Information:
The authors greatly appreciate the work of the anonymous referee, whose comments and suggestions have helped to improve the paper in many aspects. The second and fourth authors have been supported by the Czech Science Foundation under the Project 16-08549S. The third author has been supported by the project CEITEC 2020 (LQ1601) with financial support from the Ministry of Education, Youth and Sports of the Czech Republic under the National Sustainability Programme II. This work was realized in CEITEC - Central European Institute of Technology with research infrastructure supported by the project CZ.1.05/1.1.00/02.0068 financed from European Regional Development Fund.
Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2019/12/1
Y1 - 2019/12/1
N2 - Linear delayed differential systems x˙i(t)=∑j=1m∑k=1rijaijk(t)xj(hijk(t)),i=1,⋯,mare considered 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 Lebesgue measurable functions. New explicit results on uniform exponential stability, depending on all delays, are derived. The conditions obtained do not require the dominance of diagonal terms over the off-diagonal terms as most of the existing stability tests for non-autonomous delay differential systems do.
AB - Linear delayed differential systems x˙i(t)=∑j=1m∑k=1rijaijk(t)xj(hijk(t)),i=1,⋯,mare considered 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 Lebesgue measurable functions. New explicit results on uniform exponential stability, depending on all delays, are derived. The conditions obtained do not require the dominance of diagonal terms over the off-diagonal terms as most of the existing stability tests for non-autonomous delay differential systems do.
KW - Conditions depending on all delays
KW - Exponential stability
KW - Linear delayed differential system
KW - Matrix measure
UR - http://www.scopus.com/inward/record.url?scp=85074852895&partnerID=8YFLogxK
U2 - 10.1007/s10884-018-9668-9
DO - 10.1007/s10884-018-9668-9
M3 - Article
AN - SCOPUS:85074852895
SN - 1040-7294
VL - 31
SP - 2095
EP - 2108
JO - Journal of Dynamics and Differential Equations
JF - Journal of Dynamics and Differential Equations
IS - 4
ER -