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

I. I. Matveeva

doi:10.1134/S1995080222020147

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

I. I. Matveeva

Differential Equations Section

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Article number	13
Pages (from-to)	3497-3504
Number of pages	8
Journal	Lobachevskii Journal of Mathematics
Volume	42
Issue number	14
DOIs	https://doi.org/10.1134/S1995080222020147
Publication status	Published - Dec 2021

Keywords

differential equation of neutral type
estimates for solutions
Lyapunov–Krasovskii functional
stability
time-varying delay
variable coefficients

OECD FOS+WOS

1.01 MATHEMATICS

State classification of scientific and technological information

27 MATHEMATICS

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10.1134/S1995080222020147

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title = "Estimates for Solutions to a Class of Nonlinear Time-Varying Delay Systems",

abstract = "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.",

keywords = "differential equation of neutral type, estimates for solutions, Lyapunov–Krasovskii functional, stability, time-varying delay, variable coefficients",

author = "Matveeva, {I. I.}",

note = "Funding Information: The study was supported by the Russian Foundation for Basic Research (project no. 18-29-10086). Publisher Copyright: {\textcopyright} 2021, Pleiades Publishing, Ltd.",

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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

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JO - Lobachevskii Journal of Mathematics

JF - Lobachevskii Journal of Mathematics

SN - 1995-0802

IS - 14

M1 - 13

ER -

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

Abstract

Keywords

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