Contributions to the Minimal Realization Problem for Descriptor Systems

In this thesis we have studied several aspects of the minimal realization problem for descriptor systems. These aspects include purely theoretical questions such as that about the order of a minimal realization of a general improper rational matrix and problems of a numerical nature, like rounding error analysis of the computing a minimal realization from a nonminimal one. We have also treated the minimal partial realization problem for general descriptor systems with application to model reduction and to generalised eigenvalue problems