Projective geometry and feedback stabilization

Abstract

The goal of this paper is to provide a geometric study of the well-posedness and stability concepts associated to the feedback control loops. The usefulness of Kleinian-view of geometry is emphasized and tools from matrix projective geometry are applied. It will be shown that Mobius transforms play a central role to arrive to the group structures that characterize the well posed and stable feedback connections of dynamic systems. The well-known Youla parametrization is obtained as a special case of this group of transforms.