TY - JOUR

T1 - Simple uniform exponential stability conditions for a system of linear delay differential equations

AU - Berezansky, Leonid

AU - Diblík, Josef

AU - Svoboda, Zdeněk

AU - Šmarda, Zdeněk

N1 - Publisher Copyright:
© 2014 Elsevier Inc. All rights reserved.

PY - 2015/1/1

Y1 - 2015/1/1

N2 - Uniform exponential stability of linear systems with time varying coefficients xi(t)=-Σj=1mΣk=1rijaijk(t)xj(hijk(t)),i=1,...,mis studied, where t≥0,m and rij,i,j=1,...,m are natural numbers, aijk:[0,∞)→R and hijk:[0,∞)→R are measurable functions. New explicit result is derived with the proof based on Bohl-Perron theorem. The resulting criterion has advantages over some previous ones in that, e.g., it involves no M-matrix to establish stability. Several useful and easily verifiable corollaries are deduced and examples are provided to demonstrate the advantage of the stability result over known results.

AB - Uniform exponential stability of linear systems with time varying coefficients xi(t)=-Σj=1mΣk=1rijaijk(t)xj(hijk(t)),i=1,...,mis studied, where t≥0,m and rij,i,j=1,...,m are natural numbers, aijk:[0,∞)→R and hijk:[0,∞)→R are measurable functions. New explicit result is derived with the proof based on Bohl-Perron theorem. The resulting criterion has advantages over some previous ones in that, e.g., it involves no M-matrix to establish stability. Several useful and easily verifiable corollaries are deduced and examples are provided to demonstrate the advantage of the stability result over known results.

KW - Bohl-Perron theorem

KW - Linear delay differential system

KW - Uniform exponential stability

UR - http://www.scopus.com/inward/record.url?scp=84911925325&partnerID=8YFLogxK

U2 - 10.1016/j.amc.2014.10.117

DO - 10.1016/j.amc.2014.10.117

M3 - Article

AN - SCOPUS:84911925325

VL - 250

SP - 605

EP - 614

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

ER -