Dichotomy and stability of disturbed systems with periodic nonlinearities

Conference Paper (2018)
Author(s)

Vera B. Smirnova (St. Petersburg State University)

A.V. Proskurnikov (TU Delft - Team Tamas Keviczky, Russian Academy of Sciences)

Natalia V. Utina (St. Petersburg State University)

Roman V. Titov (St. Petersburg State University)

Research Group
Team Tamas Keviczky
Copyright
© 2018 Vera B. Smirnova, A.V. Proskurnikov, Natalia V. Utina, Roman V. Titov
DOI related publication
https://doi.org/10.1109/MED.2018.8443008
More Info
expand_more
Publication Year
2018
Language
English
Copyright
© 2018 Vera B. Smirnova, A.V. Proskurnikov, Natalia V. Utina, Roman V. Titov
Research Group
Team Tamas Keviczky
Pages (from-to)
903-908
ISBN (print)
978-1-5386-7890-9
Reuse Rights

Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.

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.

Files

Dichotomy_and_Stability_of_Dis... (pdf)
(pdf | 1.26 Mb)
- Embargo expired in 17-08-2021
License info not available