## 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=(v_{1},..., 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 those sets in the space of all autoregressive systems.

Original language | English |
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Pages (from-to) | 295-308 |

Number of pages | 14 |

Journal | Circuits, Systems, and Signal Processing |

Volume | 13 |

Issue number | 2-3 |

DOIs | |

State | Published - Jun 1994 |