Dichotomy and Stability of Disturbed Systems with Periodic Nonlinearities

Vera B. Smirnova, Anton V. Proskurnikov, Natalia V. Utina, Roman V. Titov

Результат исследований: Публикации в книгах, отчётах, сборниках, трудах конференцийстатья в сборнике материалов конференции

3 Цитирования (Scopus)

Аннотация

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.

Язык оригиналаанглийский
Название основной публикацииMED 2018 - 26th Mediterranean Conference on Control and Automation
ИздательInstitute of Electrical and Electronics Engineers Inc.
Страницы903-908
Число страниц6
ISBN (печатное издание)9781538678909
DOI
СостояниеОпубликовано - 20 авг 2018
Событие26th Mediterranean Conference on Control and Automation, MED 2018 - Zadar, Хорватия
Продолжительность: 19 июн 201822 июн 2018

Конференция

Конференция26th Mediterranean Conference on Control and Automation, MED 2018
СтранаХорватия
ГородZadar
Период19/06/1822/06/18

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Предметные области Scopus

  • Искусственный интеллект
  • Системотехника
  • Общее машиностроение
  • Теория оптимизации

Цитировать

Smirnova, V. B., Proskurnikov, A. V., Utina, N. V., & Titov, R. V. (2018). Dichotomy and Stability of Disturbed Systems with Periodic Nonlinearities. В MED 2018 - 26th Mediterranean Conference on Control and Automation (стр. 903-908). [8443008] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/MED.2018.8443008