Abstract
In this letter we consider nonlinear maps G(·) that are shift invariant and have “approximately-finite memory” in a certain very reasonable sense. These maps, which are assumed to satisfy a mild continuity condition, take a subset S of R into R, where R is the set of real-valued maps defined on Ƶn (as usual, Ƶ is the set of integers and n is an arbitrary positive integer). We describe results which show that all such maps can be approximated arbitrarily well, in the sense of uniform approximation, by the maps of certain special nonlinear structures. This is of interest in connection with nonlinear filtering, system identification, and the general understanding of nonlinear systems.
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