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.
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
\Bibitem{LakLinRus19}
\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}
Linking options:
https://www.mathnet.ru/eng/sjim1040
https://www.mathnet.ru/eng/sjim/v22/i2/p27
This publication is cited in the following 4 articles:
A. V. Lakeev, Yu. E. Linke, V. A. Rusanov, “Rayleigh–Ritz operator in inverse problems for higher order multilinear nonautonomous evolution equations”, Siberian Adv. Math., 33:4 (2023), 329–337
V. A. Rusanov, A. V. Lakeyev, A. V. Banshchikov, A. V. Daneev, “On the Bilinear Second Order Differential Realization of an Infinite-Dimensional Dynamical System: An Approach Based on Extensions to M2-Operators”, Fractal Fract, 7:4 (2023), 310
A.V.Lakeev, Yu. È Linke, V. A. Rusanov, “Metric properties of the Rayleigh–Ritz operator”, Russian Math. (Iz. VUZ), 66:9 (2022), 46–53
Vyacheslav Rusanov, Aleksey Daneev, Anatoliy Lakeyev, Yurij Linke, “To Existence of a Nonstationary Quasi-Linear Vector Field Realizing the Expansion of a Control Trajectory Bundle in Hilbert Space”, WSEAS TRANSACTIONS ON SYSTEMS, 19 (2020), 115
Citation in format AMSBIB
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