A homeomorphism between observable pairs and conditioned invariant subspaces

P. A. Fuhrmann; U. Helmke

doi:10.1016/S0167-6911(97)00013-3

A homeomorphism between observable pairs and conditioned invariant subspaces

P. A. Fuhrmann, U. Helmke

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

A bijective correspondence between similarity classes of observable systems (C, A) and n-codimensional conditioned invariant subspaces of a pair (script C sign, script A sign) is constructed that leads to a homeomorphism of the spaces. This is applied to the parametrization of inner functions of fixed McMillan degree. Proofs using state space methods as well as using polynomial models are given.

Original language	English
Pages (from-to)	217-223
Number of pages	7
Journal	Systems and Control Letters
Volume	30
Issue number	5
DOIs	https://doi.org/10.1016/S0167-6911(97)00013-3
State	Published - 1 Jan 1997

Keywords

Conditioned invariant subspaces
Geometric control
Inner functions
Parametrization problems

ASJC Scopus subject areas

Control and Systems Engineering
General Computer Science
Mechanical Engineering
Electrical and Electronic Engineering

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10.1016/S0167-6911(97)00013-3

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abstract = "A bijective correspondence between similarity classes of observable systems (C, A) and n-codimensional conditioned invariant subspaces of a pair (script C sign, script A sign) is constructed that leads to a homeomorphism of the spaces. This is applied to the parametrization of inner functions of fixed McMillan degree. Proofs using state space methods as well as using polynomial models are given.",

keywords = "Conditioned invariant subspaces, Geometric control, Inner functions, Parametrization problems",

author = "Fuhrmann, {P. A.} and U. Helmke",

note = "Funding Information: * Corresponding author, 1 Partially supported by GIF under Grant No. I 184. 2 Earl Katz Family Ch~Jr in Algebraic System Theory.",

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AU - Helmke, U.

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Y1 - 1997/1/1

N2 - A bijective correspondence between similarity classes of observable systems (C, A) and n-codimensional conditioned invariant subspaces of a pair (script C sign, script A sign) is constructed that leads to a homeomorphism of the spaces. This is applied to the parametrization of inner functions of fixed McMillan degree. Proofs using state space methods as well as using polynomial models are given.

AB - A bijective correspondence between similarity classes of observable systems (C, A) and n-codimensional conditioned invariant subspaces of a pair (script C sign, script A sign) is constructed that leads to a homeomorphism of the spaces. This is applied to the parametrization of inner functions of fixed McMillan degree. Proofs using state space methods as well as using polynomial models are given.

KW - Conditioned invariant subspaces

KW - Geometric control

KW - Inner functions

KW - Parametrization problems

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JO - Systems and Control Letters

JF - Systems and Control Letters

IS - 5

ER -

A homeomorphism between observable pairs and conditioned invariant subspaces

Abstract

Keywords

ASJC Scopus subject areas

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