Characterization of minimal spectral factors via homeomorphic maps

Author

Ferrante, Augusto

Author_Institution

Dipt. di Ingegneria Elettrica Gestionale e Meccanica, Udine Univ., Italy

Volume

5

fYear

1997

fDate

10-12 Dec 1997

Firstpage

4816

Abstract

In this paper a new characterization of the class of all minimal square spectral factors of a given rational spectral density is presented. This characterization consists of two bijective maps which relate the set of minimal square spectral factors to a set of invariant subspaces of a certain matrix and to a set of symmetric solutions of an algebraic Riccati equation. In the second part of the paper it is proven that these two maps are homeomorphisms. This result extends to spectral factorization theory the results of Wimmer (1995), where it is proven that the well known relation between solutions of ARE and invariant subspaces of a certain matrix is, in fact, a homeomorphism

Keywords

Riccati equations; matrix decomposition; ARE; algebraic Riccati equation; bijective maps; homeomorphic maps; homeomorphism; invariant subspaces; matrix subspaces; minimal square spectral factors characterization; rational spectral density; symmetric solutions; Circuits; Control theory; Filtering; Linear matrix inequalities; Nonlinear filters; Optimal control; Prediction theory; Riccati equations; Symmetric matrices; Topology;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 1997., Proceedings of the 36th IEEE Conference on

Conference_Location

San Diego, CA

ISSN

0191-2216

Print_ISBN

0-7803-4187-2

Type

conf

DOI

10.1109/CDC.1997.649783

Filename

649783