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 presented. 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. With regard to background material, functional power series of the form * T h e material given in this paper was described in the writer's "Conference Course" at the 1981 European Conference on Circuit Theory and Design, T h e Hague, August 1981.