Conditions for the Existence of Two Limit Cycles in a System with Hysteresis Nonlinearity

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Conditions for the Existence of Two Limit Cycles in a System with Hysteresis Nonlinearity. / Zviagintceva, T. E.; Pliss, Victor A.

In: Vestnik St. Petersburg University: Mathematics, Vol. 51, No. 3, 31.07.2018, p. 237-243.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{55b7e8b495054767b6599a43f85c8441,

title = "Conditions for the Existence of Two Limit Cycles in a System with Hysteresis Nonlinearity",

abstract = "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.",

keywords = "limit sycles, hysteresis nonlinearity, limit cycles, hysteresis nonlinearity, hysteretic system, Second Lyapunov method",

author = "Zviagintceva, {T. E.} and Pliss, {Victor A.}",

note = "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",

year = "2018",

month = jul,

day = "31",

language = "English",

volume = "51",

pages = "237--243",

journal = "Vestnik St. Petersburg University: Mathematics",

issn = "1063-4541",

publisher = "Pleiades Publishing",

number = "3",

}

RIS

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