TY - JOUR

T1 - Estimates for Solutions to a Class of Nonlinear Time-Varying Delay Systems

AU - Matveeva, I. I.

N1 - Funding Information: The study was supported by the Russian Foundation for Basic Research (project no. 18-29-10086). Publisher Copyright: © 2021, Pleiades Publishing, Ltd.

PY - 2021/12

Y1 - 2021/12

N2 - We consider a class of nonlinear systems of nonautonomous differential equations of neutral type with a time-varying delay that can be unbounded. Using a Lyapunov–Krasovskii functional, we establish some estimates of solutions that allow us to conclude whether the solutions are stable. In the case of exponential and asymptotic stability, we point out stabilization rates of the solutions at infinity.

AB - We consider a class of nonlinear systems of nonautonomous differential equations of neutral type with a time-varying delay that can be unbounded. Using a Lyapunov–Krasovskii functional, we establish some estimates of solutions that allow us to conclude whether the solutions are stable. In the case of exponential and asymptotic stability, we point out stabilization rates of the solutions at infinity.

KW - differential equation of neutral type

KW - estimates for solutions

KW - Lyapunov–Krasovskii functional

KW - stability

KW - time-varying delay

KW - variable coefficients

UR - http://www.scopus.com/inward/record.url?scp=85127428190&partnerID=8YFLogxK

UR - https://elibrary.ru/item.asp?id=48154963

U2 - 10.1134/S1995080222020147

DO - 10.1134/S1995080222020147

M3 - Article

AN - SCOPUS:85127428190

VL - 42

SP - 3497

EP - 3504

JO - Lobachevskii Journal of Mathematics

JF - Lobachevskii Journal of Mathematics

SN - 1995-0802

IS - 14

M1 - 13

ER -