  A detailed expose of the Hopf algebra approach to interconnected input-output
systems in nonlinear control theory is presented. The focus is on input-output
systems that can been represented in terms of Chen-Fliess functional expansions
or Fliess operators. This provides a starting point for a discrete-time version
of this theory. In particular, the notion of a discrete-time Fliess operator is
given and a class of parallel interconnections is described.
