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

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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.",

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language = "English (US)",

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

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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.

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

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