TOPOLOGICAL CONSIDERATIONS FOR AUTOREGRESSIVE SYSTEMS WITH FIXED KRONECKER INDEXES

In this paper we will study topological properties of the class of pro per and improper p x m transfer functions of a fixed McMillan degree n . A natural generalization of this class is all autoregressive systems of degree n under external system equivalence. The subset of irreduci ble systems has in a natural way the structure of a manifold and we sh ow how to extend this topology to the set of all autoregressive system s of degree at most n. We will describe the subset of systems with fix ed Kronecker indices v = (v1 ,..., v(p)) as an orbit space, which will enable us to calculate the topological dimension for each collection of indices v. Finally, we will describe the topological closure of tho se sets in the space of all autoregressive systems.