title: An extended class of stabilizable uncertain systems
metadata.name: dc.contributor.author
metadata.value: Zuber, Irina E.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Voloshinova, Tatiana V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Gelig, Arkadii Kh.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2016-09-28T15:48:22Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2016-09-28T15:48:22Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2016-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Zuber I. E., Voloshinova T.V., Gelig A.Kh. An extended class of stabilizable uncertain systems. Vestnik of Saint Petersburg University. Series 1. Mathematics. Mechanics. Astronomy, 2016, vol. 3 (61), issue 3, pp. 402–407.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2016.307
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/3909
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The system
  dx
  dt
  = A(·)x + B(·)u,
  u = S
  ∗
  (·)x,
  where A(·) ∈ Rn×n, B(·) ∈ Rn×m, S(·) ∈ Rn×m is considered. Elements of matrixes A(·), B(·), S(·)
  are uniformly bounded and they are functionals of arbitrary origin. It is supposed that among elements
  placed on right from principal diagonal k elements αiljl (·) (l ∈ 1, k) have constant sign and each of these
  elements is only one in his linene and his column. Other elements placed on right from principal diagonal
  are sufficiently small. It is also supposed that m = n − k and elements βij(·) of matrix B(·) have the
  following property
  inf
  (·)
  |βiss(·)| = β0 > 0 for is ∈ 1, n \{i1, . . . , ik}.
  Other elements of matrix B(·) are zeroes.
  Positive definite matrix H = {hij} of a special form is constructed. Positive numbers hii = hi are
  placed on principal diagonal, hiljl = hjlil = −0, 5 hilhjl sign αiljl (·). Other elements of matrix H are
  zeroes. Investigating the derivation of Lyapunov function V (x) = x∗H−1x we have such hi (i ∈ 1, n) and
  λi   0 (i ∈ 1, n) that for
  S(·) = H
  −1ΛB(·), Λ = diag (λ1, . . . , λn)
  the system is globally exponentially stable. The control is robust in relation to elements of matrix A(·).
  Refs 4.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: Работа выполнена при финансовой поддержке РФФИ (проект 14-01-00107) и СПбГУ (тема 6.38.230.2015).
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 1. Mathematics. Mechanics. Astronomy;Issue 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: uncertain systems stabilization
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: global exponential stability
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: An extended class of stabilizable uncertain systems
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: Zuber.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/3909/1/Zuber.pdf
resources.format: Adobe PDF
resources.size: 217,73 kB