On the metric property of an LTV generalisation of the ν-gap

Sei Zhen Khong; Michael Cantoni

doi:10.1109/CDC.2012.6427107

On the metric property of an LTV generalisation of the ν-gap

Sei Zhen Khong, Michael Cantoni

Research output: Contribution to journal › Conference article › peer-review

2 Scopus citations

Abstract

A recent linear time-varying (LTV) generalisation of Vinnicombe's ν-gap metric is defined in terms of normalised strong representations of system graphs and a Fredholm index constraint on a family of Toeplitz-Wiener-Hopf operators, parameterised by start time. It is shown in this paper that the LTV definition is invariant with respect to the choice of graph representations and that it is indeed a metric. For a class of time-invariant systems, the generalised ν-gap reduces to the original frequency-domain definition.

Original language	English (US)
Article number	6427107
Pages (from-to)	214-219
Number of pages	6
Journal	Proceedings of the IEEE Conference on Decision and Control
DOIs	https://doi.org/10.1109/CDC.2012.6427107
State	Published - 2012
Externally published	Yes
Event	51st IEEE Conference on Decision and Control, CDC 2012 - Maui, HI, United States Duration: Dec 10 2012 → Dec 13 2012

Keywords

linear time-varying systems
strong graph representations
ν-gap metric

Publisher link

10.1109/CDC.2012.6427107

Find It

Find It at U of M Libraries

Cite this

@article{af719b2870ee4ddbb237cd9faaf555cc,

title = "On the metric property of an LTV generalisation of the ν-gap",

abstract = "A recent linear time-varying (LTV) generalisation of Vinnicombe's ν-gap metric is defined in terms of normalised strong representations of system graphs and a Fredholm index constraint on a family of Toeplitz-Wiener-Hopf operators, parameterised by start time. It is shown in this paper that the LTV definition is invariant with respect to the choice of graph representations and that it is indeed a metric. For a class of time-invariant systems, the generalised ν-gap reduces to the original frequency-domain definition.",

keywords = "linear time-varying systems, strong graph representations, ν-gap metric",

author = "Khong, {Sei Zhen} and Michael Cantoni",

year = "2012",

doi = "10.1109/CDC.2012.6427107",

language = "English (US)",

pages = "214--219",

journal = "Proceedings of the IEEE Conference on Decision and Control",

issn = "0743-1546",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

note = "51st IEEE Conference on Decision and Control, CDC 2012 ; Conference date: 10-12-2012 Through 13-12-2012",

}

TY - JOUR

T1 - On the metric property of an LTV generalisation of the ν-gap

AU - Khong, Sei Zhen

AU - Cantoni, Michael

PY - 2012

Y1 - 2012

N2 - A recent linear time-varying (LTV) generalisation of Vinnicombe's ν-gap metric is defined in terms of normalised strong representations of system graphs and a Fredholm index constraint on a family of Toeplitz-Wiener-Hopf operators, parameterised by start time. It is shown in this paper that the LTV definition is invariant with respect to the choice of graph representations and that it is indeed a metric. For a class of time-invariant systems, the generalised ν-gap reduces to the original frequency-domain definition.

AB - A recent linear time-varying (LTV) generalisation of Vinnicombe's ν-gap metric is defined in terms of normalised strong representations of system graphs and a Fredholm index constraint on a family of Toeplitz-Wiener-Hopf operators, parameterised by start time. It is shown in this paper that the LTV definition is invariant with respect to the choice of graph representations and that it is indeed a metric. For a class of time-invariant systems, the generalised ν-gap reduces to the original frequency-domain definition.

KW - linear time-varying systems

KW - strong graph representations

KW - ν-gap metric

UR - http://www.scopus.com/inward/record.url?scp=84874251093&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84874251093&partnerID=8YFLogxK

U2 - 10.1109/CDC.2012.6427107

DO - 10.1109/CDC.2012.6427107

M3 - Conference article

AN - SCOPUS:84874251093

SN - 0743-1546

SP - 214

EP - 219

JO - Proceedings of the IEEE Conference on Decision and Control

JF - Proceedings of the IEEE Conference on Decision and Control

M1 - 6427107

T2 - 51st IEEE Conference on Decision and Control, CDC 2012

Y2 - 10 December 2012 through 13 December 2012

ER -

On the metric property of an LTV generalisation of the ν-gap

Abstract

Keywords

Publisher link

Find It

Other files and links

Fingerprint

Cite this