On the implementation of the superposition principle for a finite beam of integral curve of a second-order bilinear system

For a finite family of controllable integral curves of the "trajectory, software-positional control" type induced in a separable Hilbert space by a certain second-order bilinear unsteady differential system (for example, hyperbolic), but with different bilinear regulators (with different operator coefficients with a single bilinear form of these regulators), we investigated solvability of the implementation of operator functions of an invariant linear regulator, in the presence of which (in the structure of this differential system) the union of these integral curves represents a family of its admissible solutions. The study is based on the analysis of continuity and semi-additivity of the nonlinear Rayleigh-Ritz functional operator. A numerical illustrative example is given.