title: A criterion of existence and uniqueness of the Lyapunov matrix for a class of time delay systems
metadata.name: dc.contributor.author
metadata.value: Egorov, Alexey V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2016-08-02T10:40:15Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2016-08-02T10:40:15Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2016-06
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/2521
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The Lyapunov matrix for systems of linear time-delay equations is a matrix-valued function
  which is a solution of a special dynamic system with some additional boundary conditions.
  This matrix allows to construct the complete type Lyapunov–Krasovskii functionals with a
  prescribed derivative, which are used successfully in analysis of behavior of time-delay systems.
  It was shown in works of Kharitonov and Chashnikov that the Lyapunov condition, that is
  the absence of opposite eigenvalues of the system, guarantees the existence and uniqueness
  of the Lyapunov matrix for systems of retarded type with multiple delays and for systems of
  neutral type with a single delay. In this contribution, we consider a linear time-invariant system
  of neutral type with two delays. It is shown that under a certain constraint the Lyapunov
  condition, that is the absence of opposite eigenvalues of the system, is also a criterion of the
  existence and uniqueness of the Lyapunov matrix. Refs 14.
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. Series 10. Applied Mathematics. Computer Science. Control Processes;Issue 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: time-delay system
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: neutral type equation
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Lyapunov matrix
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: A criterion of existence and uniqueness of the Lyapunov matrix for a class of time delay systems
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: Егоров.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/2521/1/%d0%95%d0%b3%d0%be%d1%80%d0%be%d0%b2.pdf
resources.format: Adobe PDF
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