On the Modeling of Systems for Identification. I: $\varepsilon $-Representations of Classes of Systems

Abstract

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