A hybrid parameterization of linear single input single output systems

We obtain a parameterization of the set of finite dimensional linear dynamical systems of unbounded McMillan degree. In this parameterization a given system is represented in a nonunique way. However, a certain notion of order is available, thereby providing a graded parameterization. An important feature is that each graded space is diffeomorphic to a Euclidean space. In view of this fact we hope that many of the local results in identification (valid only if the parameter space is Euclidean) an actually be generalized globally. Moreover we show that the topology induced on the space of all plants by this space is finer than the graph topology.