ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Conditions for the Existence of a Limit Cycle in a Class of Systems with Hysteresis Nonlinearity

Author(s):

Tatiana Zviagintceva

Faculty of Mathematics and Mechanics
St. Petersburg State University
Universitetsky prospekt, 28,
Peterhof, St. Petersburg,
198504 Russia

zv_tatiana@mail.ru

Abstract:

The class of two-dimensional control systems with hysteresis nonlinearity is considered. We assume that the nonlinearity does not satisfy the sectoral condition, and is piecewise linear approximated. The coefficient conditions for the existence of limit cycles are stated by the comparison systems method.

References:

  1. Leonov G. A., Shumafov M. M., Teshev V. A. Ustoichivost system s gisterezisom. [Stability of systems with a hysteresis. ] St. Petersburg, Maikop: Adyghe State University Publ., 2012, 182 p. (In Russ. )
  2. Zvyagintseva T. E. [Global stability of automatic control systems with hysteresis nonlinearity. ] Differencial'nie uravnenia i processy upravlenia, 2013, no. 4 (In Russ. ) Available at: http://www.math.spbu.ru/diffjournal/pdf/zvyagintseva.pdf
  3. Zvyagintseva T. E. [Absolute stability of control systems with hysteresis. ] Differencial'nie uravnenia i processy upravlenia, 2014, no. 2 (In Russ. ) Available at: http://www.math.spbu.ru/diffjournal/pdf/zvyagintseva2.pdf

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