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Conditions for the Existence of Two Limit Cycles in a System with Hysteresis Nonlinearity. / Zviagintceva, T. E.; Pliss, Victor A.
в: Vestnik St. Petersburg University: Mathematics, Том 51, № 3, 31.07.2018, стр. 237-243.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - Conditions for the Existence of Two Limit Cycles in a System with Hysteresis Nonlinearity
AU - Zviagintceva, T. E.
AU - Pliss, Victor A.
N1 - Zvyagintseva, T.E., Pliss, V.A. Conditions for the Existence of Two Limit Cycles in a System with Hysteresis Nonlinearity. Vestnik St.Petersb. Univ.Math. 51, 237–243 (2018). https://doi.org/10.3103/S1063454118030135
PY - 2018/7/31
Y1 - 2018/7/31
N2 - This work deals with a two-dimensional automatic control system containing a single nonlinear hysteretic element in the general form. The conditions sufficient for the existence of at least two limit cycles in the system are presented. To prove the existence of cycles, three closed contours embedded into each other are constructed on the phase manifold by “sewing” together pieces of the level lines of various Lyapunov functions. System trajectories cross the inner contour “from outside inwards” and the middle contour “from inside outwards.” The outer contour is crossed by system trajectories “from outside inwards.” The existence of these contours proves the presence of at least two limit cycles in the system. This paper is a continuation of our earlier published work “Conditions for the Global Stability of a Single System with Hysteresis Nonlinearity,” in which the conditions of global stability in this system are formulated.
AB - This work deals with a two-dimensional automatic control system containing a single nonlinear hysteretic element in the general form. The conditions sufficient for the existence of at least two limit cycles in the system are presented. To prove the existence of cycles, three closed contours embedded into each other are constructed on the phase manifold by “sewing” together pieces of the level lines of various Lyapunov functions. System trajectories cross the inner contour “from outside inwards” and the middle contour “from inside outwards.” The outer contour is crossed by system trajectories “from outside inwards.” The existence of these contours proves the presence of at least two limit cycles in the system. This paper is a continuation of our earlier published work “Conditions for the Global Stability of a Single System with Hysteresis Nonlinearity,” in which the conditions of global stability in this system are formulated.
KW - limit sycles
KW - hysteresis nonlinearity
KW - limit cycles
KW - hysteresis nonlinearity
KW - hysteretic system
KW - Second Lyapunov method
M3 - Article
VL - 51
SP - 237
EP - 243
JO - Vestnik St. Petersburg University: Mathematics
JF - Vestnik St. Petersburg University: Mathematics
SN - 1063-4541
IS - 3
ER -
ID: 38793892