Conditions for the equivalence between IQC and graph separation stability results

Joaquin Carrasco, Peter Seiler

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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)2899-2906
Number of pages8
JournalInternational Journal of Control
Volume92
Issue number12
DOIs
StatePublished - Dec 2 2019

Bibliographical note

Funding Information:
The first author acknowledges William Heath for fruitful discussions and comments.

Keywords

  • IQC theorem
  • graph separation
  • multipliers factorisations

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