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Fundam. Prikl. Mat., 2005, Volume 11, Issue 8, Pages 105–117 (Mi fpm921)  

This article is cited in 4 scientific papers (total in 4 papers)

Singular sets and dynamic properties of bilinear control systems

V. N. Zhermolenko

Gubkin Russian State University of Oil and Gas

Abstract: The paper deals with qualitative methods of investigation of dynamic systems with control. Classification of singular sets of two-dimensional bilinear control systems is proposed. Constructive criteria of presence of different kinds of singular sets in the phase portrait are obtained. Dependence of dynamic properties of systems such as oscillation, stability, instability, and controllability on the types of singular sets is investigated. Analytical conditions under which analysis of above properties is relatively simple are obtained.

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English version:
Journal of Mathematical Sciences (New York), 2007, 147:2, 6623–6630

Bibliographic databases:

UDC: 531.3:62-50

Citation: V. N. Zhermolenko, “Singular sets and dynamic properties of bilinear control systems”, Fundam. Prikl. Mat., 11:8 (2005), 105–117; J. Math. Sci., 147:2 (2007), 6623–6630

Citation in format AMSBIB
\Bibitem{Zhe05}
\by V.~N.~Zhermolenko
\paper Singular sets and dynamic properties of bilinear control systems
\jour Fundam. Prikl. Mat.
\yr 2005
\vol 11
\issue 8
\pages 105--117
\mathnet{http://mi.mathnet.ru/fpm921}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2226754}
\zmath{https://zbmath.org/?q=an:1151.93366}
\transl
\jour J. Math. Sci.
\yr 2007
\vol 147
\issue 2
\pages 6623--6630
\crossref{https://doi.org/10.1007/s10958-007-0498-2}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-35549006722}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Zhermolenko V.N., “Trajectory funnels of two-dimensional bilinear control systems”, Journal of Computer and Systems Sciences International, 45:2 (2006), 191–203  crossref  mathscinet  zmath  isi
    2. Zhermolenko V.N., “Phase portraits of two-dimensional bilinear control systems”, Journal of Computer and Systems Sciences International, 45:3 (2006), 345–355  crossref  mathscinet  zmath  isi
    3. V. N. Zhermolenko, “Periodic motions and criteria of absolute stability, instability, and controllability of two-dimensional bilinear systems”, Autom. Remote Control, 67:8 (2006), 1194–1214  mathnet  crossref  mathscinet  zmath
    4. E. K. Kornoushenko, “Upravlenie ravnovesnymi sostoyaniyami bilineinykh normirovannykh modelei”, Probl. upravl., 5 (2012), 2–8  mathnet
  • Фундаментальная и прикладная математика
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