It is shown how non-square implicit descriptions can be used for modelling broad classes of linear systems, including systems with internal switches. 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). The objective here is to 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 a hidden way) by the degree of freedom. It is shown how to embed the variable internal structure present in square implicit descriptions inside an (A, E, B) invariant subspace contained in the kernel of the output map. Owing to this embedding, the variable internal structure is made unobservable and in this way a proper closed-loop system with a controllable pre specified structure is obtained. (C) 2003 Elsevier Ltd. All rights reserved.