Non square implicit descriptions can be used for modelling a set of linear systems, characterized by a certain common structure. Necessary and sufficient conditions, expressed in terms of the overall implicit model, exist for controlling it so that it has a unique behaviour (whatever be the internal structure variations). We enhance from these conditions the parts which are due to the common internal dynamic equation and, respectively, to the algebraic constraints which are “controlled” (in an hidden way) by the degree of freedom.