Homotopy for the ν-gap

Thomas Brinsmead; Brian Anderson

doi:10.4310/CIS.2001.v1.n4.a1

Homotopy for the ν-gap

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

Abstract

The main result of this paper is to show that a “winding number condition” which relates to two strictly multivariable linear operators, and which is used in the definition of the Vinnicombe (ν-gap) metric, is equivalent to the existence of a multivariable homotopy in the same metric between the two operators. This allows a characterisation of the Vinnicombe metric which is independent of the linearity of the underlying operators, and suggests possible extension of the metric to nonlinear operators.

Original language	English
Pages (from-to)	333-380
Journal	Communications in Information and Systems
Volume	1
Issue number	4
DOIs	https://doi.org/10.4310/CIS.2001.v1.n4.a1
Publication status	Published - Dec 2001

Access to Document

10.4310/CIS.2001.v1.n4.a1

Cite this

@article{1515a860f82e46a69d1f19d8953fe062,

title = "Homotopy for the ν-gap",

abstract = "The main result of this paper is to show that a “winding number condition” which relates to two strictly multivariable linear operators, and which is used in the definition of the Vinnicombe (ν-gap) metric, is equivalent to the existence of a multivariable homotopy in the same metric between the two operators. This allows a characterisation of the Vinnicombe metric which is independent of the linearity of the underlying operators, and suggests possible extension of the metric to nonlinear operators.",

author = "Thomas Brinsmead and Brian Anderson",

year = "2001",

month = dec,

doi = "10.4310/CIS.2001.v1.n4.a1",

language = "English",

volume = "1",

pages = "333--380",

journal = "Communications in Information and Systems",

issn = "2163-4548",

publisher = "International Press",

number = "4",

}

TY - JOUR

T1 - Homotopy for the ν-gap

AU - Brinsmead, Thomas

AU - Anderson, Brian

PY - 2001/12

Y1 - 2001/12

N2 - The main result of this paper is to show that a “winding number condition” which relates to two strictly multivariable linear operators, and which is used in the definition of the Vinnicombe (ν-gap) metric, is equivalent to the existence of a multivariable homotopy in the same metric between the two operators. This allows a characterisation of the Vinnicombe metric which is independent of the linearity of the underlying operators, and suggests possible extension of the metric to nonlinear operators.

AB - The main result of this paper is to show that a “winding number condition” which relates to two strictly multivariable linear operators, and which is used in the definition of the Vinnicombe (ν-gap) metric, is equivalent to the existence of a multivariable homotopy in the same metric between the two operators. This allows a characterisation of the Vinnicombe metric which is independent of the linearity of the underlying operators, and suggests possible extension of the metric to nonlinear operators.

U2 - 10.4310/CIS.2001.v1.n4.a1

DO - 10.4310/CIS.2001.v1.n4.a1

M3 - Article

SN - 2163-4548

VL - 1

SP - 333

EP - 380

JO - Communications in Information and Systems

JF - Communications in Information and Systems

IS - 4

ER -

Homotopy for the ν-gap

Abstract

Access to Document

Fingerprint

Cite this