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

Authors
  • Kuptsova, S. E.1
  • Stepenko, N. A.2
  • Kuptsov, S. Yu.1
  • 1 St. Petersburg State University, St. Petersburg, Russia , St. Petersburg (Russia)
  • 2 OOO OGS RUSSIA, St. Petersburg, Russia , St. Petersburg (Russia)
Type
Published Article
Journal
Automation and Remote Control
Publisher
Pleiades Publishing
Publication Date
Jun 11, 2019
Volume
80
Issue
6
Pages
1016–1025
Identifiers
DOI: 10.1134/S000511791906002X
Source
Springer Nature
Keywords
License
Yellow

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.

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