title: The stability of differential-difference equations with proportional time delay. I. Linear controlled system
metadata.name: dc.contributor.author
metadata.value: Ekimov, Alexander V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Zhabko, Aleksei P.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Yakovlev, Pavel V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2020-11-19T14:14:04Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2020-11-19T14:14:04Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2020-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Ekimov A. V., Zhabko A. P., Yakovlev P. V. The stability of differential-difference equations with proportional time delay. I. Linear controlled system. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2020, vol. 16, iss. 3, pp. 316–325.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu10.2020.308
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/20757
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The article considers a controlled system of linear differential-difference equations with a
  linearly increasing delay. Sufficient conditions for the asymptotic stability of such systems
  are known; however, general conditions for the stabilizability of controlled systems and
  constructive algorithms for constructing stabilizing controls have not yet been obtained.
  For a linear differential-difference equation of delayed type with linearly increasing delay, the
  canonical Zubov transformation is applied and conditions for the stabilization of such systems
  by static control are derived. An algorithm for checking the conditions for the existence of a
  stabilizing control and for its constructing is formulated. New theorems on stability analysis
  of systems of linear differential-difference equations with linearly increasing delay are proven.
  The results obtained can be applied to the case of systems with several proportional delays.
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. Applied Mathematics. Computer Science. Control Processes;Volume 16; Issue 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: system of linear differential-difference equations
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: linearly increasing time delay
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: asymptotic stability
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: stabilizing control
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: asymptotic evaluation system
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: The stability of differential-difference equations with proportional time delay. I. Linear controlled system
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 316-325.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/20757/1/316-325.pdf
resources.format: Adobe PDF
resources.size: 247 kB