Title
Dichotomy and stability of disturbed systems with periodic nonlinearities
Author
Smirnova, Vera B. (St. Petersburg State University)
Proskurnikov, A.V. (TU Delft Team Tamas Keviczky; Russian Academy of Sciences)
Utina, Natalia V. (St. Petersburg State University)
Titov, Roman V. (St. Petersburg State University)
Date
2018
Abstract
Systems that can be decomposed as feedback interconnections of stable linear blocks and periodic nonlinearities arise in many physical and engineering applications. The relevant models e.g. describe oscillations of a viscously damped pendulum, synchronization circuits (phase, frequency and delay locked loops) and networks of coupled power generators. A system with periodic nonlinearities usually has multiple equilibria (some of them being locally unstable). Many tools of classical stability and control theories fail to cope with such systems. One of the efficient methods, elaborated to deal with periodic nonlinearities, stems from the celebrated Popov method of 'integral indices', or integral quadratic constraints; this method leads, in particular, to frequency-domain criteria of the solutions' convergence, or, equivalently, global stability of the equilibria set. In this paper, we further develop Popov's method, addressing the problem of robustness of the convergence property against external disturbances that do not oscillate at infinity (allowing the system to have equilibria points). Will the forced solutions also converge to one of the equilibria points of the disturbed system? In this paper, a criterion for this type of robustness is offered.
Subject
Convergence
Frequency-domain analysis
Circuit stability
Stability criteria
Synchronization
To reference this document use:
http://resolver.tudelft.nl/uuid:5dfcc581-1d83-46a3-a354-c147037d0427
DOI
https://doi.org/10.1109/MED.2018.8443008
Publisher
IEEE, Piscataway, NJ, USA
Embargo date
2021-08-17
ISBN
978-1-5386-7890-9
Source
Proceedings of the 26th Mediterranean Conference on Control and Automation (MED 2018)
Event
MED 2018: 26th Mediterranean Conference on Control and Automation, 2018-06-19 → 2018-06-22, Zadar, Croatia
Bibliographical note
Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.
Part of collection
Institutional Repository
Document type
conference paper
Rights
© 2018 Vera B. Smirnova, A.V. Proskurnikov, Natalia V. Utina, Roman V. Titov