Conditions for the equivalence between IQC and graph separation stability results. Issue 12 (2nd December 2019)

• Record Type: Journal Article
• Authors: Carrasco, Joaquin; Seiler, Peter
• Is Part Of: International journal of control. Volume 92:Issue 12(2019)
• Page Start: 2899
• Page End: 2906
• Publication Date: 2019-12-02
• Subjects: IQC theorem -- graph separation -- multipliers factorisations; Automatic control -- Periodicals; Electronic journals; 629.8
• DOI: 10.1080/00207179.2018.1465205
• Languages: English
• ISSNs: 0020-7179

Abstract

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.