The asymptotic stability of a nonstationary system with delay

In this paper we study the exponential stability of a linear system of differential equations with a constant delay such that the right-hand side of one of its subsystems contains an exponential multiplier. We establish sufficient conditions for the existence of an asymptotically periodic solution to the inhomogeneous system. © 2013 Allerton Press, Inc

Асимптотические свойства и стабилизация одной системы нейтрального типа с постоянным запаздыванием

The problem of obtaining sufficient conditions for the asymptotic stability for a certain class of linear systems of a neutral type with constant delay is analyzed in the article. Some coefficients of these systems in the right side have an exponential factor. As a consequence, the study of the stability of such systems with the help of the Lyapunov-Krasovskii functionals is not possible; methods of receiving asymptotic appreciations lead to extremely rough results. By applying the apparatus of difference systems and the properties of simpler systems, which the author examined previous, sufficient conditions for the exponential stability of such systems are obtained. As an example, a second-order system is considered. The graphs of the solutions of the corresponding system, both without neutral members and with the original system where the right-hand side contains neutral terms, are provided. On the basis of theory difference systems, the author proposes an algorithm of stabilization for some systems of a similar type. © 2021 Saint Petersburg State University. All rights reserved

Stabilization of some systems with constant delay

An algorithm for stabilization of a class of systems with constant delay is proposed. © 201

The first-approximation stability of a nonstationary system with delay

We study the exponential stability of a nonlinear system of differential equations with constant delay such that the right-hand side of one of its subsystems contains the multiplier e t. We obtain a sufficient condition for the first-approximation stability of this system. © 2012. Allerton Press, Inc