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arXiv · 1704.04816

Conditions for the equivalence between IQC and graph separation stability results

Joaquin Carrasco·Peter Seiler
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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.

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Joaquin Carrasco, Peter Seiler. 2017-04-16. Conditions for the equivalence between IQC and graph separation stability results. https://doi.org/10.1080/00207179.2018.1465205

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