Expansions for Nonlinear Systems*

In this paper we study operator-type models of dynamic nonlinear physical systems, such as communication channels and control systems. Attention is focused on the problem of determining conditions under which there exists a power-series-like expansion, or a polynomial-type approximation, for a system's outputs in terms of its inputs. Related problems concerning properties of the expansions are also considered and nonlocal, as well as local, results are given. In particular, we show for the first time the existence of a locally convergent Volterra-series representation for the input-output relation of an important large class of nonlinear systems containing an arbitrary finite number of nonlinear elements.