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Avtomat. i Telemekh., 2019, Issue 6, Pages 38–50 (Mi at15075)  

Nonlinear Systems

Sufficient conditions for the existence of asymptotic quiescent position for one class of differential-difference systems

S. E. Kuptsovaa, N. A. Stepenkoa, S. Yu. Kuptsovb

a St. Petersburg State University, St. Petersburg, Russia
b OOO OGS RUSSIA, St. Petersburg, Russia

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.

DOI: https://doi.org/10.1134/S0005231019060023

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English version:
Automation and Remote Control, 2019, 80:6, 1016–1025

Bibliographic databases:

Document Type: Article

Received: 01.06.2018
Revised: 03.07.2018
Accepted: 08.11.2018

Citation: S. E. Kuptsova, N. A. Stepenko, S. Yu. Kuptsov, “Sufficient conditions for the existence of asymptotic quiescent position for one class of differential-difference systems”, Avtomat. i Telemekh., 2019, no. 6, 38–50; Autom. Remote Control, 80:6 (2019), 1016–1025

Citation in format AMSBIB
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