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

Sei Zhen Khong, Michael Cantoni

Research output: Contribution to journalConference articlepeer-review

3 Scopus citations


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 languageEnglish (US)
Article number6427107
Pages (from-to)214-219
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
StatePublished - Dec 1 2012
Event51st IEEE Conference on Decision and Control, CDC 2012 - Maui, HI, United States
Duration: Dec 10 2012Dec 13 2012


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


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