Conditions for the equivalence between IQC and graph separation stability results

Joaquin Carrasco, Peter Seiler

    Research output: Contribution to journalArticlepeer-review

    82 Downloads (Pure)

    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” factorizations of the multiplier, considering only one of the two frequency-domain conditions. Here it is shown that a symmetric, “doubly-hard” factorization is required to convert both frequency-domain conditions into truncated time-domain conditions. By using the appropriate factorization, 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
    JournalInternational Journal of Control
    Early online date18 Apr 2018
    DOIs
    Publication statusPublished - 2018

    Keywords

    • IQC theorem
    • graph separation
    • multipliers factorizations

    Fingerprint

    Dive into the research topics of 'Conditions for the equivalence between IQC and graph separation stability results'. Together they form a unique fingerprint.

    Cite this