title: Conditions for the two limit cycles existence in a system with hysteresis nonlinearity
metadata.name: dc.contributor.author
metadata.value: Zviagitceva, Tatiana E.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Pliss, Viktor A.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2018-09-18T11:34:55Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2018-09-18T11:34:55Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2018-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Zviagitceva T. E., Pliss V.A. Conditions for the two limit cycles existence in a system with hysteresis nonlinearity. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2018, vol. 5 (63), issue 3, pp. 402–410.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2018.304
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/14883
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: In this paper, a two-dimensional automatic control system containing a single nonlinear
  hysteresis element of the general form is considered. Phase space of the system is a manifold
  with boundary consisting of two connected sheets. Existence of manifold boundary is
  conditioned by the motion of the phase point along hysteresis loop. This work is a continuation
  of the paper “Conditions for the global stability of a single system with hysteresis
  nonlinearity” published previously by the authors, where it is shown that under some conditions
  on the functions defining hysteresis such system is in a way globally stable. This paper
  presents sufficient conditions for considered system to have at least two limit cycles. Three
  closed contours embedded into each other are constructed in order to prove the existence
  of cycles on the phase manifold. The contours are composed of the pieces of the level lines
  of various Lyapunov functions. The inner contour is crossed by system trajectories from
  the outside to the inside, the middle contour is crossed by the trajectories from the inside
  to the outside. The outer contour is crossed by the system trajectories from the outside to
  the inside. The existence of such contours proves the presence of at least two limit cycles
  in the system.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: Работа выполнена при частичной финансовой поддержке РФФИ (грант № 16-01-00452).
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 5(63); Issue 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: system with hysteresis
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: limit cycle
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Lyapunov’s second method
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Conditions for the two limit cycles existence in a system with hysteresis nonlinearity
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 04-Zvyagintseva.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/14883/1/04-Zvyagintseva.pdf
resources.format: Adobe PDF
resources.size: 532,94 kB