Path-connectedness of frequency-domain uncertainty sets in the graph topology

Sei Zhen Khong, Michael Cantoni, Ulf T. Jönsson

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations


Path-connectedness with respect to the topology induced by the ν-gap metric underpins a recent robustness result for uncertain feedback interconnections of transfer functions in the Callier-Desoer algebra; i.e. possibly distributed-parameter with only finitely many unstable poles. In this paper, we establish path-connectedness of the following uncertainty sets of such transfer functions: diagonally structured sets with path-connected entries; arbitrarily large H- norm balls; and suficiently small ν-gap metric balls. Proof of the latter relies on the existence of a certain J-spectral factorisation, which is also established herein.

Original languageEnglish (US)
Title of host publicationProceedings of the 18th IFAC World Congress
PublisherIFAC Secretariat
Number of pages6
Edition1 PART 1
ISBN (Print)9783902661937
StatePublished - 2011

Publication series

NameIFAC Proceedings Volumes (IFAC-PapersOnline)
Number1 PART 1
ISSN (Print)1474-6670

Bibliographical note

Funding Information:
★This work was supported in part by the Australian Research Council (DP0880494).


  • Distributed-parameter uncertainty
  • Feedback
  • Path-connectedness
  • ν-gap metric

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