Z(+) fading memory and extensions of input-output maps

Much is known about time-invariant non-linear systems with inputs and outpu ts defined on Y+ that possess approximately-finite memory. For example, und er mild additional conditions, they can be approximated arbitrarily well by the maps of certain interesting simple structures. An important fact that gives meaning to results concerning such systems is that the approximately- finite-memory condition is known to be often met. Here we consider the know n proposition that if a causal time-invariant discrete-time input-output ma p H has fading memory on a set of bounded functions defined on all of the i ntegers Y, then H can be approximated arbitrarily well by a finite Volterra series operator. We show that in a certain sense, involving the existence of extensions of system maps, this result too has wide applicability. Copyr ight (C) 2001 John Wiley & Sons, Ltd.