Generating series for networks of Chen–Fliess series

Abstract

Consider a set of single-input, single-output nonlinear systems whose input–output maps are described only in terms of convergent Chen–Fliess series without any assumption that finite dimensional state space models are available. It is shown that any additive or multiplicative interconnection of such systems always has a Chen–Fliess series representation that can be computed explicitly in terms of iterated formal Lie derivatives.