Vestnik Sankt-Peterburgskogo Universiteta. Seriya 10. Prikladnaya Matematika. Informatika. Protsessy Upravleniya
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Vestnik Sankt-Peterburgskogo Universiteta. Seriya 10. Prikladnaya Matematika. Informatika. Protsessy Upravleniya, 2023, Volume 19, Issue 1, Pages 4–9
DOI: https://doi.org/10.21638/11701/spbu10.2023.101 (Mi vspui562) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Applied mathematics

The stability of differential-difference systems with linearly increasing delay. II. Systems with additive right side

A. V. Ekimov, A. P. Zhabko, P. V. Yakovlev

St. Petersburg State University, 7–9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation
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DOI: https://doi.org/10.21638/11701/spbu10.2023.101
Abstract: The article considers an uncontrolled system of differential-difference equations with a homogeneous additive right side and linearly increasing delay. Sufficient conditions for asymptotic stability are known for a number of special cases of such systems. Razumikhin's theorem on the asymptotic stability of homogeneous systems with proportional delay is formulated. Sufficient conditions for asymptotic stability are obtained basing on the asymptotic stability of the initial system without delay and constructing the Lyapunov function.
Keywords: system of linear differential-differencel equations, linearly increasing, time delay, asymptotic stability, homogeneous system.
Received: December 26, 2022
Accepted: January 19, 2023
Document Type: Article
UDC: 517.929
MSC: 34K20
Language: Russian
Citation: A. V. Ekimov, A. P. Zhabko, P. V. Yakovlev, “The stability of differential-difference systems with linearly increasing delay. II. Systems with additive right side”, Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 19:1 (2023), 4–9
Citation in format AMSBIB
\Bibitem{EkiZhaYak23}
\by A.~V.~Ekimov, A.~P.~Zhabko, P.~V.~Yakovlev
\paper The stability of differential-difference systems with linearly increasing delay. II.~Systems with additive right side
\jour Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr.
\yr 2023
\vol 19
\issue 1
\pages 4--9
\mathnet{http://mi.mathnet.ru/vspui562}
\crossref{https://doi.org/10.21638/11701/spbu10.2023.101}
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    		Вестник Санкт-Петербургского университета. Серия 10. Прикладная математика. Информатика. Процессы управления
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