Uniform approximation of time-invariant non-linear systems

It is shown that the elements of a large class of time-invariant non-linear input-output maps can be uniformly approximated arbitrarily well, over infinite time intervals, using a certain structure that can be implemented in many ways using, for example, radial basis functions, polynomial functions, piecewise linear functions, sigmoids, or combinations of these functions. For the special case in which these functions are taken to be certain polynomial functions, the input-output map of our structure is a generalized finite Volterra series. Results are given for the case in which inputs and outputs are defined on R. The case in which inputs and outputs are defined on the half-line R+ is also addressed, and in both cases inputs need not be functions that are continuous. Copyright (C) 2004 John Wiley Sons, Ltd.