Abstract:
Based on perturbation theory methods, criteria for the Lyapunov stability of Lurie systems with weakly oscillating parameters are proposed. The main attention is paid to obtaining the first approximation formulas for perturbations of multiple definite and indefinite multipliers of linear Hamiltonian systems and their applications to stability analysis. The formulas proposed lead to new criteria for the Lyapunov stability of Lurie systems in critical cases. Applications to the problem of a parametric resonance in fundamental resonances are considered. The results obtained are stated in terms of the original equations and brought to the stage of design formulas and algorithms. The efficiency of the formulas is illustrated by the example of the problem on the parametric resonance in a system of coupled oscillators.
Keywords:
Hamiltonian system, Lurie system, stability, small parameter, parametric resonance.
The research by A.S. Belova was carried out within the framework of the state order
from the Ministry of Science and Higher Education of the Russian Federation, scientific topic code
no. FZWU-2020-0027.
Presented by the member of Editorial Board:A. I. Malikov
Citation:
M. G. Yumagulov, L. S. Ibragimova, A. S. Belova, “Investigation of the problem on a parametric resonance in Lurie systems with weakly oscillating coefficients”, Avtomat. i Telemekh., 2022, no. 2, 107–121; Autom. Remote Control, 83:2 (2022), 252–263
\Bibitem{YumIbrBel22}
\by M.~G.~Yumagulov, L.~S.~Ibragimova, A.~S.~Belova
\paper Investigation of the problem on a parametric resonance in Lurie systems with weakly oscillating coefficients
\jour Avtomat. i Telemekh.
\yr 2022
\issue 2
\pages 107--121
\mathnet{http://mi.mathnet.ru/at15897}
\crossref{https://doi.org/10.31857/S0005231022020076}
\transl
\jour Autom. Remote Control
\yr 2022
\vol 83
\issue 2
\pages 252--263
\crossref{https://doi.org/10.1134/S0005117922020072}
Linking options:
https://www.mathnet.ru/eng/at15897
https://www.mathnet.ru/eng/at/y2022/i2/p107
This publication is cited in the following 3 articles:
M. G. Yumagulov, L. S. Ibragimova, “Equivalent Differential Equations in Problems of Control Theory
and the Theory of Hamiltonian Systems”, Diff Equat, 60:1 (2024), 23
M. G Yumagulov, L. S Ibragimova, “EKVIVALENTNYE DIFFERENTsIAL'NYE URAVNENIYa V ZADAChAKh TEORII UPRAVLENIYa I TEORII GAMIL'TONOVYKh SISTEM”, Differencialʹnye uravneniâ, 60:1 (2024), 24
M. G. Yumagulov, L. S. Ibragimova, “Equivalent Hamiltonian Systems for Differential Equations with Even Order Derivatives”, Lobachevskii J Math, 45:6 (2024), 2792
Citation in format AMSBIB
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