Complex scaling circle criteria for Luré systems

• Published in: International journal of control Vol. 92; no. 5; pp. 975 - 986
• Main Author: Zhou, J.
• Format: Journal Article
• Language: English
• 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
• ISSN: 0020-7179; 1366-5820
• DOI: 10.1080/00207179.2017.1378439

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.