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Sibirskii Zhurnal Industrial'noi Matematiki, 2019, Volume 22, Number 2, Pages 27–36
DOI: https://doi.org/10.17377/sibjim.2019.22.203 (Mi sjim1040) 		 
This article is cited in 4 scientific papers (total in 4 papers)

On the differential realization of a second-order bilinear system in a Hilbert space

A. V. Lakeyeva, Yu. E. Linkeb, V. A. Rusanova

a Matrosov Institute for System Dynamics and Control Theory SB RAS, ul. Lermontova 134, 664033 Irkutsk
b Irkutsk National Research Technical University, ul. Lermontova 83, 664074 Irkutsk
Full-text PDF (261 kB) Citations (4)
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DOI: https://doi.org/10.17377/sibjim.2019.22.203
Abstract: We study the necessary and sufficient conditions for the existence of a nonlinear differential realization of a continuous infinite-dimensional behaviorist system in the class of nonstationary second-order bilinear ordinary differential (in particular, hyperbolic) equations in a separable Hilbert space. The obtained conditions rely upon the tensor products of Hilbert spaces. In passing, we analytically justify some topological-metrical continuity conditions for the projectivization of the Rayleigh–Ritz operator with the calculation of the fundamental group of its image.
Keywords: inverse problem of nonlinear system analysis, bilinear differential realization.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00301
19-08-00746
Received: 12.07.2018
Revised: 10.12.2018
Accepted: 27.12.2018
English version:
Journal of Applied and Industrial Mathematics, 2019, Volume 13, Issue 2, Pages 261–269
DOI: https://doi.org/10.1134/S1990478919020078
Bibliographic databases:
Document Type: Article
UDC: 517.93:517.937
Language: Russian
Citation: A. V. Lakeyev, Yu. E. Linke, V. A. Rusanov, “On the differential realization of a second-order bilinear system in a Hilbert space”, Sib. Zh. Ind. Mat., 22:2 (2019), 27–36; J. Appl. Industr. Math., 13:2 (2019), 261–269
Citation in format AMSBIB
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\by A.~V.~Lakeyev, Yu.~E.~Linke, V.~A.~Rusanov
\paper On the differential realization of a second-order bilinear system in a Hilbert space
\jour Sib. Zh. Ind. Mat.
\yr 2019
\vol 22
\issue 2
\pages 27--36
\mathnet{http://mi.mathnet.ru/sjim1040}
\crossref{https://doi.org/10.17377/sibjim.2019.22.203}
\elib{https://elibrary.ru/item.asp?id=41688466}
\transl
\jour J. Appl. Industr. Math.
\yr 2019
\vol 13
\issue 2
\pages 261--269
\crossref{https://doi.org/10.1134/S1990478919020078}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85067409007}
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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