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 - 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 -