Topological considerations for autoregressive systems with fixed Kronecker indices

Joachim Rosenthal, Michael Sain, Xiaochang Wang

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

In this paper we will study topological properties of the class of proper and improper p×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 irreducible systems has in a natural way the structure of a manifold and we show how to extend this topology to the set of all autoregressive systems of degree at most n. We will describe the subset of systems with fixed Kronecker indices v=(v1,..., vp) 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 those sets in the space of all autoregressive systems.

Original languageEnglish
Pages (from-to)295-308
Number of pages14
JournalCircuits, Systems, and Signal Processing
Volume13
Issue number2-3
DOIs
StatePublished - Jun 1994

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