Sufficient Conditions for the Existence of Asymptotic Quiescent Position for One Class of Differential-Difference Systems

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Sufficient Conditions for the Existence of Asymptotic Quiescent Position for One Class of Differential-Difference Systems. / Kuptsova, S. E.; Stepenko, N. A.; Kuptsov, S. Yu.

в: Automation and Remote Control, Том 80, № 6, 01.06.2019, стр. 1016-1025.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{c1b75454bf404623b905ca2a98a29bcc,

title = "Sufficient Conditions for the Existence of Asymptotic Quiescent Position for One Class of Differential-Difference Systems",

abstract = "The time-delay systems are considered and the limiting behavior of their solutions is investigated. The case in which the solutions have the trivial equilibrium that may not be an invariant set of the system is studied. The notion of an asymptotic quiescent position for the trajectories of delayed systems is introduced. Its stability is analyzed by the method of Lyapunov functions using the Razumikhin approach. Sufficient conditions for the existence of an asymptotic quiescent position for one class of the systems of differential-difference equations are established. Some illustrative examples of nonlinear differential equations with delay that have an asymptotic quiescent position are given and the sufficient conditions are applied to them.",

keywords = "asymptotic quiescent position, Lyapunov function, Lyapunov stability, nonlinear time-delay systems, Razumikhin approach",

author = "Kuptsova, {S. E.} and Stepenko, {N. A.} and Kuptsov, {S. Yu}",

year = "2019",

month = jun,

day = "1",

doi = "10.1134/S000511791906002X",

language = "English",

volume = "80",

pages = "1016--1025",

journal = "Automation and Remote Control",

issn = "0005-1179",

publisher = "МАИК {"}Наука/Интерпериодика{"}",

number = "6",

}

RIS

TY - JOUR

T1 - Sufficient Conditions for the Existence of Asymptotic Quiescent Position for One Class of Differential-Difference Systems

AU - Kuptsova, S. E.

AU - Stepenko, N. A.

AU - Kuptsov, S. Yu

PY - 2019/6/1

Y1 - 2019/6/1

N2 - The time-delay systems are considered and the limiting behavior of their solutions is investigated. The case in which the solutions have the trivial equilibrium that may not be an invariant set of the system is studied. The notion of an asymptotic quiescent position for the trajectories of delayed systems is introduced. Its stability is analyzed by the method of Lyapunov functions using the Razumikhin approach. Sufficient conditions for the existence of an asymptotic quiescent position for one class of the systems of differential-difference equations are established. Some illustrative examples of nonlinear differential equations with delay that have an asymptotic quiescent position are given and the sufficient conditions are applied to them.

AB - The time-delay systems are considered and the limiting behavior of their solutions is investigated. The case in which the solutions have the trivial equilibrium that may not be an invariant set of the system is studied. The notion of an asymptotic quiescent position for the trajectories of delayed systems is introduced. Its stability is analyzed by the method of Lyapunov functions using the Razumikhin approach. Sufficient conditions for the existence of an asymptotic quiescent position for one class of the systems of differential-difference equations are established. Some illustrative examples of nonlinear differential equations with delay that have an asymptotic quiescent position are given and the sufficient conditions are applied to them.

KW - asymptotic quiescent position

KW - Lyapunov function

KW - Lyapunov stability

KW - nonlinear time-delay systems

KW - Razumikhin approach

UR - http://www.scopus.com/inward/record.url?scp=85067012000&partnerID=8YFLogxK

U2 - 10.1134/S000511791906002X

DO - 10.1134/S000511791906002X

M3 - Article

AN - SCOPUS:85067012000

VL - 80

SP - 1016

EP - 1025

JO - Automation and Remote Control

JF - Automation and Remote Control

SN - 0005-1179

IS - 6

ER -

ID: 51338424