B. G. Grebenshchikov, S. A. Zagrebina, A. B. Lozhnikov, “Methods for studying the asymptotic properties and stabilization of some systems with linear delay”, J. Comp. Eng. Math., 2025, Volume 12, Issue 3,Pages <nobr>14

Computational Mathematics

Methods for studying the asymptotic properties and stabilization of some systems with linear delay

B. G. Grebenshchikov^a, S. A. Zagrebina^a, A. B. Lozhnikov^bc

^a South Ural State University, Chelyabinsk, Russian Federation
^b N.N. Krasovskii Institute of Mathematics and Mechanics, Ekaterinburg, Russian Federation
^c Ural Federal University, Ekaterinburg, Russian Federation

Abstract: Methods for obtaining sufficient conditions of asymptotic stability and instability for systems of differential equations containing linear delay are proposed. Based on these conditions, some systems of linear differential equations are investigated, one of them is stabilized over an infinite period of time.

Keywords: asymptotic stability, linear delay, stabilization.

UDC: 519.6

MSC: 93D15

Received: 30.07.2025

Language: English

DOI: 10.14529/jcem250302