Journal of Applied and Industrial Mathematics

, Volume 13, Issue 2, pp 261–269 | Cite as

On the Differential Realization of a Second-Order Bilinear System in a Hilbert Space

  • A. V. LakeyevEmail author
  • Yu. E. LinkeEmail author
  • V. A. RusanovEmail author


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.


inverse problem of nonlinear system analysis bilinear differential realization 


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© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Matrosov Institute for System Dynamics and Control TheoryIrkutskRussia
  2. 2.Irkutsk National Research Technical UniversityIrkutskRussia

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