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Automation and Remote Control

, Volume 80, Issue 6, pp 1016–1025 | Cite as

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

  • S. E. KuptsovaEmail author
  • N. A. Stepenko
  • S. Yu. Kuptsov
Nonlinear Systems
  • 2 Downloads

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

Lyapunov stability nonlinear time-delay systems asymptotic quiescent position Lyapunov function Razumikhin approach 

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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  • S. E. Kuptsova
    • 1
    Email author
  • N. A. Stepenko
    • 2
  • S. Yu. Kuptsov
    • 1
  1. 1.St. Petersburg State UniversitySt. PetersburgRussia
  2. 2.OOO OGS RUSSIASt. PetersburgRussia

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