Almost stabilizability subspaces and high gain feedback

The class of "almost stabilizability subspaces" is introduced as the state-space analog of the class of stable, but not necessarily proper, transfer functions. Almost stabilizability subspaces can be considered as candidate closed-loop eigenspaces associated with infinitely fast and stable modes. We derive the basic properties of these subspaces, and show that they can be approximated by regular stabilizability subspaces. The relation with high gain feedback is elaborated upon in a number of applications.