title: On the problem of Aizerman: Coefficient conditions for an existence of three-period and six-period сycles in a second-order discrete-time system
metadata.name: dc.contributor.author
metadata.value: Zvyagintseva, Tatiana E.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2020-05-28T17:47:44Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2020-05-28T17:47:44Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2020-06
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Zvyagintseva Т. Е. On the problem of Aizerman: Coefficient conditions for an existence of three-period and six-period сycles in a second-order discrete-time system. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2020, vol. 7 (65), issue 2, pp. 309–318.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu01.2020.213
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/17946
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: In this paper, an automatic control discrete-time system of the second order is studied. Nonlinearity
  of this system satisfies the generalized Routh—Hurwitz condition. Systems of this
  type are widely used in solving modern applied problems of the theory of automatic control.
  This work is a continuation of the research presented in the author’s paper “On the problem
  of Aizerman: Coefficient conditions for an existence of four-period cycle in a second-order
  discrete-time system”, where systems with two-periodic nonlinearity lying in the Hurwitz
  angle are studied. In the referenced paper, the conditions on the parameters under which a
  system with two-periodic nonlinearity can have a family of non-isolated four-period cycles
  are indicated and a method for constructing such nonlinearity is proposed. In this paper, it
  is assumed that the nonlinearity is three-periodic and lies in the Hurwitz angle. The system
  is studied for all possible values of the parameters. We explicitly indicate the conditions
  on the parameters under which it is possible to construct such a three-periodic nonlinearity
  that the system with specified nonlinearity is not globally asymptotically stable. It is
  shown that a family of three-period cycles and a family of six-period cycles can exist in
  the system with indicated nonlinearity. A method for constructing such nonlinearities is
  proposed. The cycles are not isolated, any solution of the system with the initial data lying
  on some specified ray is periodic.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: The work is supported in part by Russian Foundation for Basic Research (grant N19-01-00388).
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 7 (65); Issue 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: second-order discrete-time system
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Aizerman conjecture
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: absolute stability
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: periodic solution
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On the problem of Aizerman: Coefficient conditions for an existence of three-period and six-period сycles in a second-order discrete-time system
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 309-318.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/17946/1/309-318.pdf
resources.format: Adobe PDF
resources.size: 309,7 kB