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Title: Asymptotic properties and stabilization of a neutral type system with constant delay
Асимптотические свойства и стабилизация одной системы нейтрального типа с постоянным запаздыванием
Authors: Grebenshchikov, B. G.
Issue Date: 2021
Publisher: Saint Petersburg State University
Citation: Grebenshchikov B. G. Asymptotic properties and stabilization of a neutral type system with constant delay / B. G. Grebenshchikov. — DOI 10.21638/11701/SPBU10.2021.108 // Vestnik Sankt-Peterburgskogo Universiteta, Prikladnaya Matematika, Informatika, Protsessy Upravleniya. — 2021. — Vol. 17. — Iss. 1. — P. 81-95.
Abstract: 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.
Keywords: CONTROL
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85106707924
PURE ID: 21884882
ISSN: 18119905
DOI: 10.21638/11701/SPBU10.2021.108
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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