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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika
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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2010, Number 12, Pages 87–90 (Mi ivm7164)  
This article is cited in 4 scientific papers (total in 4 papers)

Brief communications

Stabilization of the second-order linear time-invariant control systems by a delayed feedback

M. M. Shumafov

Adygeya State University, Maikop, Republic of Adygeya, Russia
Full-text PDF (149 kB) Citations (4)
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Abstract: We consider a static stabilization problem for a two-dimensional linear time-invariant control system with a delayed feedback. We obtain the necessary and sufficient conditions for the stabilizability of the system under consideration. The theorems proved in this paper show that such a delayed feedback approach is efficient in stabilizing the second-order linear systems.
Keywords: linear time-invariant system, delayed feedback, stationary stabilization, asymptotic stability.
Received: 27.04.2010
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2010, Volume 54, Issue 12, Pages 76–78
DOI: https://doi.org/10.3103/S1066369X10120091
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: M. M. Shumafov, “Stabilization of the second-order linear time-invariant control systems by a delayed feedback”, Izv. Vyssh. Uchebn. Zaved. Mat., 2010, no. 12, 87–90; Russian Math. (Iz. VUZ), 54:12 (2010), 76–78
Citation in format AMSBIB
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\by M.~M.~Shumafov
\paper Stabilization of the second-order linear time-invariant control systems by a~delayed feedback
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2010
\issue 12
\pages 87--90
\mathnet{http://mi.mathnet.ru/ivm7164}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2814582}
\elib{https://elibrary.ru/item.asp?id=15208514}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2010
\vol 54
\issue 12
\pages 76--78
\crossref{https://doi.org/10.3103/S1066369X10120091}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79952825586}
Linking options:
  • https://www.mathnet.ru/eng/ivm7164
  • https://www.mathnet.ru/eng/ivm/y2010/i12/p87
    • This publication is cited in the following 4 articles:
    1. I. V. Boykov, N. P. Krivulin, “Methods for Control of Dynamical Systems with Delayed Feedback”, J Math Sci, 255:5 (2021), 561  crossref
    2. G. A. Leonov, M. M. Shumafov, “Pyragas stabilizability of unstable equilibria by nonstationary time-delayed feedback”, Autom. Remote Control, 79:6 (2018), 1029–1039  mathnet  crossref  isi  elib
    3. Shumafov M.M., “Ob usloviyakh stabiliziruemosti trekhmernykh lineinykh sistem”, Vestnik adygeiskogo gosudarstvennogo universiteta. seriya 4: estestvenno-matematicheskie i tekhnicheskie nauki, 2012, no. 3, 57–63  elib
    4. Leonov G.A., Shumafov M.M., “Vibrational stabilization and the Brockett problem”, Differ. Equ., 47:13 (2011), 1853–1915  crossref  mathscinet  zmath  isi  elib  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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    Abstract page:754
    Full-text PDF :281
    References:69
    First page:4
     
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