  This study investigates a parameterization of all output-rectifying retrofit
controllers for distributed design of a structured controller. It has been
discovered that all retrofit controllers can be characterized as a constrained
Youla parameterization, which is difficult to solve analytically. For
synthesis, a tractable and insightful class of retrofit controllers, referred
to as output-rectifying retrofit controllers, has been introduced. An
unconstrained parameterization of all output-rectifying retrofit controllers
can be derived under a technical assumption on measurability of particular
signals. The aim of this note is to reveal the structure of all
output-rectifying retrofit controllers in the general output-feedback case. It
is found out that the existing developments can be generalized based on the
notions of state projection and an inverse system. The result leads to the
conclusion that output-rectifying retrofit controllers can readily be designed
even in the general case.
