Representations of nonlinear systems via the stone-weierstrass theorem

The Stone-Weierstrass theorem is extended and used to develop a general theorem on representations of bounded, continuous, time-invariant, causal nonlinear systems which allows one to construct representations with desired structural properties. The general theorem encompasses the classic series of Volterra, Wiener, and Barrett as well as Zadeh's hierarchy. Application to system identification is discussed.

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