TY - JOUR
T1 - Asymptotic properties of neutral type linear systems
AU - Berezansky, Leonid
AU - Braverman, Elena
N1 - Funding Information:
E. Braverman was partially supported by NSERC , the grant RGPIN-2020-03934 . The authors are very grateful to the anonymous referees whose thoughtful comments significantly contributed to the quality of presentation.
Publisher Copyright:
© 2020 Elsevier Inc.
PY - 2021/5/15
Y1 - 2021/5/15
N2 - Exponential stability and solution estimates are investigated for a delay system x˙(t)−A(t)x˙(g(t))=∑k=1mBk(t)x(hk(t)) of a neutral type, where A and Bk are n×n bounded matrix functions, and g,hk are delayed arguments. Stability tests are applicable to a wide class of linear neutral systems with time-varying coefficients and delays. In addition, explicit exponential estimates for solutions of both homogeneous and non-homogeneous neutral systems are obtained for the first time. These inequalities are not just asymptotic estimates, they are valid on every finite segment and evaluate both short- and long-term behavior of solutions.
AB - Exponential stability and solution estimates are investigated for a delay system x˙(t)−A(t)x˙(g(t))=∑k=1mBk(t)x(hk(t)) of a neutral type, where A and Bk are n×n bounded matrix functions, and g,hk are delayed arguments. Stability tests are applicable to a wide class of linear neutral systems with time-varying coefficients and delays. In addition, explicit exponential estimates for solutions of both homogeneous and non-homogeneous neutral systems are obtained for the first time. These inequalities are not just asymptotic estimates, they are valid on every finite segment and evaluate both short- and long-term behavior of solutions.
KW - Exponential estimates of solutions
KW - Exponential stability
KW - Linear neutral delay system
KW - Matrix measure
KW - Non-autonomous system
UR - http://www.scopus.com/inward/record.url?scp=85098562627&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2020.124893
DO - 10.1016/j.jmaa.2020.124893
M3 - Article
AN - SCOPUS:85098562627
SN - 0022-247X
VL - 497
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
M1 - 124893
ER -