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.
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
\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://mathscinet.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{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-35549006722}
Linking options:
https://www.mathnet.ru/eng/fpm921
https://www.mathnet.ru/eng/fpm/v11/i8/p105
This publication is cited in the following 5 articles:
Victor Zhermolenko, Alexander Poznyak, “Criteria of robust stability for time-varying 2D Wang–Mitchel differential systems: integral funnel method”, International Journal of Control, 89:11 (2016), 2297
E. K. Kornoushenko, “Upravlenie ravnovesnymi sostoyaniyami bilineinykh normirovannykh modelei”, Probl. upravl., 5 (2012), 2–8
Zhermolenko V.N., “Trajectory funnels of two-dimensional bilinear control systems”, Journal of Computer and Systems Sciences International, 45:2 (2006), 191–203
Zhermolenko V.N., “Phase portraits of two-dimensional bilinear control systems”, Journal of Computer and Systems Sciences International, 45:3 (2006), 345–355
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
Citation in format AMSBIB
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