Gap metrics for time-varying linear systems in a continuous-time setting

Sei Zhen Khong, Michael Cantoni

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


A recently proposed time-varying generalisation of Vinnicombe's ν-gap is shown to have the properties of a metric on a class of causal linear continuous-time systems that admit normalised strong graph representations. An alternative time-varying gap metric is then defined in more general terms and a corresponding robust stability result is derived for linear feedback interconnections. Finally, it is shown that the time-varying gap and ν-gap metrics induce the same topology, this being the coarsest topology under which feedback stability and closed-loop sensitivity are both robust properties.

Original languageEnglish (US)
Pages (from-to)118-126
Number of pages9
JournalSystems and Control Letters
StatePublished - Aug 2014
Externally publishedYes

Bibliographical note

Funding Information:
This work was supported by the Swedish Research Council through the LCCC Linnaeus centre and the Australian Research Council ( DP130104510 ). This paper was not presented at any IFAC meeting.


  • Feedback
  • Linear time-varying systems
  • Robust stability


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