NOTES ON UNIFORM APPROXIMATION OF SHIFT-VARYING SYSTEMS

It is shown that the elements G of a large class of input-output maps can be uniformly approximated arbitrarily well using a certain structu re if and only if G is continuous. For the case considered the system inputs and outputs are defined on a discrete set {0, 1, ..., a(1)} x . .. x {0, 1, ..., a(m)}, in which a(1), ..., a(m) are positive integers . Our approximating structure involves certain functions that can be c hosen in different ways. 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 discrete Volterra series. Our results provide an analytical basis for the use of such series.