title: Stabilization of some class of uncertain systems
metadata.name: dc.contributor.author
metadata.value: Zakharenkov, Maksim S.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2018-04-26T09:23:57Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2018-04-26T09:23:57Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2018-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Zakharenkov M. S. Stabilization of some class of uncertain systems. Vestnik SPbSU. Mathematics. Mechanics. Astronomy, 2018, vol. 5 (63), issue 1, pp. 51–59.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2018.106
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/9498
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: Consider the problem of stabilizing control u synthesis for systems
  dx
  dt
  = Ax + Bu,
  where A ∈ Rn×n,B ∈ Rn×m. Elements  i,j(·) of matrix A are uniformly bounded functionals
  of arbitrary nature. In case of continuous system matrix B elements are also continuous
  and uniformly bounded functionals. In case of pulse-modulated system matrix B elements
  are differentiable uniformly bounded functions of time. Assumed that k isolated uniformly
  bounded elements  il,jl (·) exist over the main diagonal of matrix A(·) such as
  inf
  (·)
  | il ,jl (·)| ≥  − > 0, l ∈ 1, k.
  Gk is a set of isolated elements existing in the system. J1 is a set of indexes of rows of matrix
  A(·), where isolated elements are located and J2 is a set of indexes of rows of matrix A(·),
  where isolated elements do not exist. Assumed that other elements located over the main
  diagonal with indexes from J1 are sufficiently small.
  sup
  (·)
  | i,j (·)| <  ,  i,j /∈ Gk, i ∈ J1, j > i.
  Other elements located over the main diagonal are uniformly bounded.
  In continuous case u = S(·)x, in pulse-modulated case u =  (t), where vector  
  components are outputs of synchronized pulse elements.
  Using construction of special quadratic Lyapunov function one can determine S(·),
  such that for continuosed case closed loop system is globally exponentially stable. In pulsemodulated
  case such output pulses are synthesised so that system is globally asymptotically
  stable.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: Работа выполнена при финансовой поддержке СПбГУ (тема 6.38.230.2015) и РФФИ (грант
  17-01-00102а).
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. Mathematics. Mechanics. Astronomy;Volume 5(63); Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: uncertain pulse-modulated systems
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: uncertain systems stabilization
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Stabilization of some class of uncertain systems
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 06-Zakharenkov.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/9498/1/06-Zakharenkov.pdf
resources.format: Adobe PDF
resources.size: 302,11 kB