title: Lyapunov matrices for a class of systems with exponential kernel
metadata.name: dc.contributor.author
metadata.value: Aliseyko, Alexey N.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2017-10-12T09:32:45Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2017-10-12T09:32:45Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2017-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Aliseyko A. N. Lyapunov matrices for a class of systems with exponential kernel. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2017, vol. 13, iss. 3, pp. 228–240.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu10.2017.301
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/8509
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The problem of computation of Lyapunov matrices arises when Lyapunov—Krasovskii
  functionals are applied for stability analysis of linear time-invariant delay systems. A Lyapunov
  matrix is a solution of a matrix time-delay differential equation that satisfies two special Lyapunov condition is satisfied, i. e. time-delay system has no eigenvalues symmetric with
  respect to the origin. Nevertheless, computational methods for Lyapunov matrices exist only
  for several classes of time-delay systems. In this contribution, we study time-delay systems
  with distributed delay and exponential kernel. In a contribution of Kharitonov, the problem of
  finding a Lyapunov matrix for this class of time-delay systems was reduced to the computation
  of solutions to an auxiliary delay-free system of ordinary differential equations with boundary
  conditions. However, the boundary conditions that were proposed earlier are not sufficient
  for the uniqueness of solutions to the auxiliary system, and results reported in the paper by
  Kharitonov do not allow us to obtain the Lyapunov matrix from a solution to an auxiliary
  system. These substantial differences between this class of time-delay systems and the wellstudied
  class of linear systems with one delay arise from ambiguity in the choice of boundary
  conditions for the auxiliary system. In this paper we propose a new set of boundary conditions
  that allows us to develop a theory similar to that of systems with one delay. It is shown that
  a solution of the auxiliary system with the new boundary conditions allows us to obtain the
  Lyapunov matrix. It is established that the auxiliary system admits a unique solution if and
  only if the Lyapunov condition is satisfied. Thus, one can verify existence and uniqueness of
  the Lyapunov matrix during its construction. Refs 12.
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 13; Issue 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: time-delay systems
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Lyapunov matrix
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Lyapunov matrices for a class of systems with exponential kernel
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 01-Aliseyko.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/8509/1/01-Aliseyko.pdf
resources.format: Adobe PDF
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