Conditions for the equivalence between IQC and graph separation stability results

Joaquin Carrasco, Peter J Seiler Jr

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

This paper provides a link between time-domain and frequency-domain stability results in the literature. Specifically, we focus on the comparison between stability results for a feedback interconnection of two nonlinear systems stated in terms of frequency-domain conditions. While the integral quadratic constrain (IQC) theorem can cope with them via a homotopy argument for the Lurye problem, graph separation results require the transformation of the frequency-domain conditions into truncated time-domain conditions. To date, much of the literature focuses on ‘hard’ factorisations of the multiplier, considering only one of the two frequency-domain conditions. Here it is shown that a symmetric, ‘doubly-hard’ factorisation is required to convert both frequency-domain conditions into truncated time-domain conditions. By using the appropriate factorisation, a novel comparison between the results obtained by IQC and separation theories is then provided. As a result, we identify under what conditions the IQC theorem may provide some advantage.

Original languageEnglish (US)
Pages (from-to)1-8
Number of pages8
JournalInternational Journal of Control
DOIs
StateAccepted/In press - Apr 1 2018

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Keywords

  • IQC theorem
  • graph separation
  • multipliers factorisations

Cite this

Conditions for the equivalence between IQC and graph separation stability results. / Carrasco, Joaquin; Seiler Jr, Peter J.

In: International Journal of Control, 01.04.2018, p. 1-8.

Research output: Contribution to journalArticle

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