  The general goal of this paper is to identify a transformation group that can
be used to describe a class of feedback interconnections involving subsystems
which are modeled solely in terms of Chen-Fliess functional expansions or
Fliess operators and are independent of the existence of any state space
models. This interconnection, called an output affine feedback connection, is
distinguished from conventional output feedback by the presence of a multiplier
in an outer loop. Once this transformation group is established, three basic
questions are addressed. How can this transformation group be used to provide
an explicit Fliess operator representation of such a closed-loop system? Is it
possible to use this feedback scheme to do system inversion purely in an
input-output setting? In particular, can feedback input-output linearization be
posed and solved entirely in this framework, i.e., without the need for any
state space realization? Lastly, what can be said about feedback invariants
under this transformation group? A final objective of the paper is to describe
the Lie algebra of infinitesimal characters associated with the group in terms
of a pre-Lie product.
