Conditions for the equivalence between IQC and graph separation stability results |
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Authors: | Joaquin Carrasco Peter Seiler |
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Affiliation: | 1. Control Systems Centre, School of Electrical and Electronic Engineering, The University of Manchester
, Manchester, UK joaquin.carrascogomez@manchester.ac.uk;3. Aerospace Engineering and Mechanics Department, University of Minnesota
, Minneapolis, MN, USA |
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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’ 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. |
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Keywords: | IQC theorem graph separation multipliers factorisations |
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