On the Differential Realization of a Second-Order Bilinear System in a Hilbert Space
- Authors: Lakeyev A.V.1, Linke Y.E.2, Rusanov V.A.1
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Affiliations:
- Matrosov Institute for System Dynamics and Control Theory
- Irkutsk National Research Technical University
- Issue: Vol 13, No 2 (2019)
- Pages: 261-269
- Section: Article
- URL: https://journals.rcsi.science/1990-4789/article/view/213171
- DOI: https://doi.org/10.1134/S1990478919020078
- ID: 213171
Cite item
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.
About the authors
A. V. Lakeyev
Matrosov Institute for System Dynamics and Control Theory
Author for correspondence.
Email: lakeyev@icc.ru
Russian Federation, ul. Lermontova 134, Irkutsk, 664033
Yu. E. Linke
Irkutsk National Research Technical University
Author for correspondence.
Email: linkeyurij@gmail.com
Russian Federation, ul. Lermontova 83, Irkutsk, 664074
V. A. Rusanov
Matrosov Institute for System Dynamics and Control Theory
Author for correspondence.
Email: v.rusanov@mail.ru
Russian Federation, ul. Lermontova 134, Irkutsk, 664033