Realization of a polylinear controller as a second-order differential system in a Hilbert space

Abstract

We study the solvability of the inverse nonlinear system analysis problem viewed as qualitative solvability (necessary and sufficient conditions) of a realization of a time-varying polylinear controller as a second-order differential system whose admissible solutions include a given nonlinear pencil of arbitrary (finite, countable, or continual) cardinality of dynamic processes in a separable Hilbert space.