On the differential simulation of the second-order bilinear system: a tensor approach

In terms of the tensor product of real Hilbert spaces, the paper provides the description of the results of a functional-geometric study of the necessary and sufficient conditions for the existence of a differential realization of a continuous infinite-dimensional dynamical system in the class of controlled bilinear nonstationary ordinary differential equations of the second order (including quasi-linear hyperbolic models) in a separable Hilbert space. Concurrently, the topological and metric conditions for the continuity of the Rayleigh - Ritz operator with the calculation of the fundamental group of its image are analytically substantiated. The results obtained give incentives for generalizations in the qualitative theory of nonlinear structural identification of higher order multi-linear differential models.