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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2023, Number 1, Pages 36–50
DOI: https://doi.org/10.26907/0021-3446-2023-1-36-50 (Mi ivm9846) 		 
On the problem of choice of methods for stabilizing systems containing linear delay

B. G. Grebenshchikova, A. B. Lozhnikovbc

a South Ural State University, 76 Lenin Ave., Chelyabinsk, 454080 Russia
b N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Science, 16 S.Kovalevskaya str., Ekaterinburg, 620108 Russia
c Ural Federal University, 19 Mira str., Ekaterinburg, 620002 Russia
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DOI: https://doi.org/10.26907/0021-3446-2023-1-36-50
Abstract: The problem of stabilization of systems of linear differential equations containing a delay linearly dependent on the argument (time) is considered. Methods of stabilization of some systems with constant coefficients are proposed. Due to the fact that the delay increases indefinitely, stabilization is considered over an infinite time interval. The numerical examples illustrating the effectiveness of stabilization methods are presented.
Keywords: time-delay, controllable system, stability, stabilization.
Received: 17.03.2022
Revised: 13.10.2022
Accepted: 21.12.2022
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2023, Volume 67, Issue 1, Pages 30–42
DOI: https://doi.org/10.3103/S1066369X23010036
Document Type: Article
UDC: 517.977
Language: Russian
Citation: B. G. Grebenshchikov, A. B. Lozhnikov, “On the problem of choice of methods for stabilizing systems containing linear delay”, Izv. Vyssh. Uchebn. Zaved. Mat., 2023, no. 1, 36–50; Russian Math. (Iz. VUZ), 67:1 (2023), 30–42
Citation in format AMSBIB
\Bibitem{GreLoz23}
\by B.~G.~Grebenshchikov, A.~B.~Lozhnikov
\paper On the problem of choice of methods for stabilizing systems containing linear delay
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2023
\issue 1
\pages 36--50
\mathnet{http://mi.mathnet.ru/ivm9846}
\crossref{https://doi.org/10.26907/0021-3446-2023-1-36-50}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2023
\vol 67
\issue 1
\pages 30--42
\crossref{https://doi.org/10.3103/S1066369X23010036}
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