title: Stability analysis of mechanical systems with distributed delay via decomposition
metadata.name: dc.contributor.author
metadata.value: Aleksandrov, Alexander Yu.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Tikhonov, Alexey A.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2021-05-04T14:08:57Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2021-05-04T14:08:57Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2021-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Aleksandrov A. Yu., Tikhonov A. A. Stability analysis of mechanical systems with distributed delay via decomposition. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2021, vol. 17, iss. 1, pp. 13–26.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu10.2021.102
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/28420
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The article analyzes a linear mechanical system with a large parameter at the vector of
  velocity forces and a distributed delay in positional forces. With the aid of the decomposition
  method, conditions are obtained under which the problem of stability analysis of the original
  system of the second-order differential equations can be reduced to studying the stability of
  two auxiliary first-order subsystems. It should be noted that one of the auxiliary subsystems
  does not contain a delay, whereas for the second subsystem containing a distributed delay,
  the stability conditions are formulated in terms of the feasibility of systems of linear matrix
  inequalities. To substantiate this decomposition, the Lyapunov direct method is used. Special
  constructions of Lyapunov—Krasovskii functionals are proposed. The developed approach is
  applied to the problem of monoaxial stabilization of a rigid body. The results of a numerical
  simulation are presented confirming the conclusions obtained analytically.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: This work was supported by the Russian Foundation for Basic Research (grant N 19-01-00146-a).
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Applied Mathematics. Computer Science. Control Processes;Volume 17; Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: mechanical system
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: stability
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: distributed delay
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: decomposition
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: rigid body
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Lyapunov—Krasovskii functionals
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Stability analysis of mechanical systems with distributed delay via decomposition
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 02_Александров.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/28420/1/02_%d0%90%d0%bb%d0%b5%d0%ba%d1%81%d0%b0%d0%bd%d0%b4%d1%80%d0%be%d0%b2.pdf
resources.format: Adobe PDF
resources.size: 320,59 kB