title: On the problem of Aizerman: coefficient conditions for an existence of four-period cycle 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: 2020-04-10T12:29:30Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2020-04-10T12:29:30Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2020-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Zvyagintseva Т. Е. On the problem of Aizerman: coefficient conditions for an existence of four-period cycle in a second-order discrete-time system. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2020, vol. 7 (65), issue 1, pp. 50–59.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu01.2020.105
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/17327
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 conditions. Systems
  of this type are widely used in solving modern applied problems that arise in engineering,
  theory of motion control, mechanics, physics and robotics. In the recent papers published
  by W. Heath, J. Carrasco, and M. de la Sen, two examples of planar discrete-time systems
  with nonlinearity that lies in the Hurwitz angle are constructed. These examples demonstrate
  that discrete-time Aizerman and Kalman conjectures are false even for second-order
  systems. One of the systems constructed by the authors has a non-trivial periodic solution
  of period three, and the other one has a non-trivial periodic solution of period four. In this
  paper, we assume that the nonlinearity is two-periodic and lies in the Hurwitz angle, and
  we study the system for all possible values of the parameters. We explicitly indicate the
  conditions for the parameters under which it is possible to construct such a two-periodic
  nonlinearity that system is not globally asymptotically stable. Indicated nonlinearity can
  be constructed in more than one way. We provide a method for its construction. We prove
  that in a system with this nonlinearity a family of non-trivial periodic solutions of period
  four exists. 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 1
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 four-period cycle in a second-order discrete-time system
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 50-59.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/17327/1/50-59.pdf
resources.format: Adobe PDF
resources.size: 4,72 MB