A polynomial approach to Hankel norm and balanced approximations

A new unified approach to problems of Hankel norm and balanced approximations is presented which is based on a combination of polynomial algebra and the geometry of invariant subspaces. Contrary to state space methods, where contact with external properties of systems is indirect, the approach presented yields new insights into basic properties of Hankel norm approximation and balanced realizations. Several approximation results are interpreted geometrically in terms of projections. Also duality results in this area are printed out.