On the stability of one equation with a discrete retarded argument and a constant concentrated delay-Reference-Cited by-同舟云学术

On the stability of one equation with a discrete retarded argument and a constant concentrated delay

Published:2023-10-27 Issue:10 Volume: Page:90-94
ISSN:2076-4626
Container-title:Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika
language:
Short-container-title:jour

Author:

Mulyukov M. V.¹

Affiliation:

1. Perm State National Research University; Perm National Research Polytechnic University

Abstract

A functional differential equation with a discrete retarded argument and a constant concentrated delay is considered. The problem of the asymptotic stability of this equation is reduced to the problem of the location of the spectrum of the shift operator. Coefficient sufficient conditions for the asymptotic stability of this equation are obtained. The domain in the parameter space such that these conditions are necessary is obtained.

Publisher

Kazan Federal University

Subject

General Earth and Planetary Sciences,General Environmental Science

Reference12 articles.

1. Kozlov R.I., Kozlova O.R. Issledovanie ustoichivosti nelineinykh nepreryvno-diskretnykh modelei ekonomicheskoi dinamiki metodom VFL. I, Izv. RAN. Teoriya i sistemy upravleniya (2), 104-113 (2009).

2. Fridman E. Stability of linear descriptor systems with delay: a Lyapunov-based approach, J. Math. Anal. and Appl. 273 (1), 24-44 (2002).

3. Kozlov R.I., Kozlova O.R. Issledovanie ustoichivosti nelineinykh nepreryvno-diskretnykh modelei ekonomicheskoi dinamiki metodom VFL. II, Izv. RAN. Teoriya i sistemy upravleniya (3), 41-50 (2009).

4. De la Sen M. Total Stability Properties Based on Fixed Point Theory for a Class of Hybrid Dynamic Systems, Hindawi Publ. Corporation Fixed Point Theory and Appl., article 826438 (2009).

5. Simonov P.M. K voprosu ob ustoichivosti sistemy dvukh lineinykh gibridnykh funktsional'no-differentsial'nykh sistem s posledeistviem, Vestn. rossiisk. un-ov. Matem. 25 (131), 299-306 (2020).