On the computation of the gap metric

Tryphon T. Georgiou

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126 Scopus citations


This paper deals with the computation of the gap metric introduced by Zames and El-Sakkary [17]. It is shown that the gap between two systems (P1, P2) is precisely the maximum of the two expressions inf Qε{lunate}H∞ Di Ni - Dj NjQ for (i, j) equal to (1, 2) and (2, 1), and (Ni, Di) being normalized right coprine factorizations of Pi, i = 1, 2, in the sense of Vidyasagar [12]. This expression is computable using well-known techniques from interpolation theory.

Original languageEnglish (US)
Pages (from-to)253-257
Number of pages5
JournalSystems and Control Letters
Issue number4
StatePublished - Oct 1988

Bibliographical note

Funding Information:
* This research was supported in part by NSF under Grant No. ECS-8705291 and MIP-8708811.


  • Gap metric
  • Graph metric
  • Topology of unstable systems


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