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

A. V. Lakeyev ; Yu. E. Linke ; V. A. Rusanov

Sibirskij žurnal industrialʹnoj matematiki, Tome 22 (2019) no. 2, pp. 27-36.

Résumé

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.

Détail

Keywords: inverse problem of nonlinear system analysis, bilinear differential realization.

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