Complex scaling circle criteria for Luré systems

This study reports alternative frequency-domain interpretation and implementation of the circle criteria for absolute stability in Luré systems by means of complex scaling and the argument principle. By Luré system, a feedback configuration with a nominal LTI model subject to sector nonlinearities i...

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Published inInternational journal of control Vol. 92; no. 5; pp. 975 - 986
Main Author Zhou, J.
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 04.05.2019
Taylor & Francis Ltd
Subjects
Circle criterion
Feedback
Frequency analysis
Frequency domain analysis
Loci
Luré problem
positive realness
return difference
Scaling
sector nonlinearity
Stability
Stability criteria
Transfer functions
Online AccessGet full text
ISSN0020-7179
1366-5820
DOI10.1080/00207179.2017.1378439

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Abstract This study reports alternative frequency-domain interpretation and implementation of the circle criteria for absolute stability in Luré systems by means of complex scaling and the argument principle. By Luré system, a feedback configuration with a nominal LTI model subject to sector nonlinearities is meant as usual. First, the complex scaling stability criterion is proved for asymptotic stability in LTI feedback connections, which dispenses open-loop poles and contour/locus pre-orientation and possesses bounded loci without prior frequency sweeping. Second, a novel frequency-domain interpretation for positive realness of transfer functions is developed and employed for claiming the complex scaling circle criteria, which accommodate various sector nonlinearities with unified conditions. The new circle criteria are conformable in both multivariable and scalar cases, implementable graphically and tractable numerically, besides being a frequency/complex-domain analytical technique. Third, the results also reveal several frequency-domain facts about Luré systems that remain unknown so far. Finally, numerical examples are included to illustrate the main results.
AbstractList This study reports alternative frequency-domain interpretation and implementation of the circle criteria for absolute stability in Luré systems by means of complex scaling and the argument principle. By Luré system, a feedback configuration with a nominal LTI model subject to sector nonlinearities is meant as usual. First, the complex scaling stability criterion is proved for asymptotic stability in LTI feedback connections, which dispenses open-loop poles and contour/locus pre-orientation and possesses bounded loci without prior frequency sweeping. Second, a novel frequency-domain interpretation for positive realness of transfer functions is developed and employed for claiming the complex scaling circle criteria, which accommodate various sector nonlinearities with unified conditions. The new circle criteria are conformable in both multivariable and scalar cases, implementable graphically and tractable numerically, besides being a frequency/complex-domain analytical technique. Third, the results also reveal several frequency-domain facts about Luré systems that remain unknown so far. Finally, numerical examples are included to illustrate the main results.
Author Zhou, J.
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  organization: Department of Automatic Control Engineering, Hohai University
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SubjectTerms Circle criterion
Feedback
Frequency analysis
Frequency domain analysis
Loci
Luré problem
positive realness
return difference
Scaling
sector nonlinearity
Stability
Stability criteria
Transfer functions
Title Complex scaling circle criteria for Luré systems
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