A description of the authors’ results bound up with the functional-geometric study of the necessary and sufficient conditions of existence of the differential realization for an infinite-dimensional dynamic system (Willems behavioral system [1]) in the class of bilinear non-stationary 2nd order ordinary differential equations (including the hyperbolic models) in the separable Hilbert space is described in terms of the tensor product of real Hilbert spaces. Side by side with solving the main problem, grounded are the topologic-metric conditions of discontinuity of projectivization of the nonlinear functional Relay-Ritz operator with computing the fundamental group of its image. The results obtained may have applications to the theory of structural identification of polylinear differential models.

inverse problems of nonlinear systems analysis, bilinear differential realization.