On the Modeling of Systems for Identification. I: ε-Representations of Classes of Systems

The notion of a class of systems is formalized. The notion of an approximating class of systems is formalized with the definitions of ε-approximations and of ε-representations. Basic properties of and relationships between ε-representations are established. A fundamental existence theorem for ε-representations is proved, as well as a theorem giving ε-representations from ε-approximations. A construction of ε-approximations using Volterra polynomials is given.