Well-posedness and generic exact controllability of coupled systems

We consider coupled systems consisting of a well-posed and strictly proper subsystem and a finite-dimensional subsystem connected in feedback. The external world interacts with the coupled system via the finite-dimensional part, which receives the external input and sends out the output. We allow the external input and the feedback signal from the infinite-dimensional part to be two separate inputs of the finite-dimensional part. We consider the output of the infinite-dimensional part as an additional output. Under several assumptions, we derive well-posedness, regularity and generic exact controllability results for such coupled systems.