title: Lyapunov’s first method: estimates of characteristic numbers of functional matrices
metadata.name: dc.contributor.author
metadata.value: Ermolin, Vladislav S.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Vlasova, Tatyana V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2020-03-05T11:46:14Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2020-03-05T11:46:14Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2019-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Ermolin V. S., Vlasova T. V. Lyapunov’s first method: estimates of characteristic numbers of functional matrices. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2019, vol. 15, iss. 4, pp. 442–456.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu10.2019.403
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/17156
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: This paper contains the development of theoretical fundamentals of the first method of
  Lyapunov. We analyze the relations between characteristic numbers of functional matrices,
  their rows, and columns. We consider Lyapunov’s results obtained to evaluate and calculate
  characteristic numbers for products of scalar functions and prove a theorem on the generalization
  of these results to the products of matrices. This theorem states necessary and
  sufficient conditions for the existence of rigorous estimates for characteristic numbers of
  matrix products. Also, we prove a theorem that establishes a relationship between the
  characteristic number of a square non-singular matrix and the characteristic number of its
  inverse matrix, and the determinant. The stated relations and properties of the characteristic
  numbers of square matrices we reformulate in terms of the Lyapunov exponents. Examples
  of matrices illustrate the proved theorems.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: en
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 15; Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: Lyapunov’s first method
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: stability theory
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: characteristic numbers
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: the Lyapunov exponent
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: functional matrices
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Lyapunov’s first method: estimates of characteristic numbers of functional matrices
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 442-456.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/17156/1/442-456.pdf
resources.format: Adobe PDF
resources.size: 328,31 kB