In this article, the concept of control system synthesis via a method using the characteristic transfer function matrix (CTFM), is explained. Then, the formal definition of CTFM and the associated concept of connectivity are presented. Next, CTFM-based control system analysis and synthesis are discussed, together with the derivation of the necessary and sufficient conditions for the realisation of a proper controller. A summary of the design procedure is presented and three design examples are introduced, in order to illustrate this procedure. Finally, the main conclusions to the work are presented.