  Introductory state-space linear control courses focus on linear,
time-invariant systems and spend intense efforts by introducing system
realizations that allow the student to grasp fundamental concepts, among which
controllability, observability, and controller and observer design. This note
describes a graphical mechanism to transform a system expressed in
observability form into its observer form based on elementary block diagram
manipulations, a technique whose pedagogical usefulness tends to be overlooked.
Given the well-known duality principle in linear systems with respect to
controllability and observability, the proposed graphical mechanism is
applicable to transform from controllability to controller realization.
