Solvability of differential realization of minimum dynamic order for a family of nonlinear input-output processes in Hilbert space

Abstract

For a family of arbitrary cardinality of input-output processes of a continuous behavioristic system with a nonlinear positional control, in the constructions of trajectorycontrol pairs we obtain a characteristic test for the existence of a differential realization of minimum dynamic order in the class of autonomous state equations in a Hilbert space.

Extension in the Hilbert Space of the Differential Realization of a Countable Set of Nonlinear “Input–Output” Processes1

“…This problem is mathematically self-sufficient since it represents an exceptional interest from the viewpoint of understanding the thin topologic-algebraic structure of the set of controlled dynamic processes possessing differential realization (1). The next productive intension in this study can be in the specification of how much the geometrical property (2) in the structure of space H 2 , which allowed deriving Theorem 2 about the one-element extension of dynamic bundle, depends on the condition T 0 = AE (mod m), including autonomous systems of realization [5].…”