Advertisement

Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Hysteresis nonstationary nonlinearities

Abstract

We consider an operator (variable hysteron) used to describe a nonstationary hysteresis nonlinearity (whose characteristics vary under the action of external forces) according to the Krasnosel’skii-Pokrovskii scheme. Sufficient conditions under which the operator is defined for the inputs from the class of functions H 1[t 0, T] satisfying the Lipschitz condition in the segment [t 0, T] are established.

This is a preview of subscription content, log in to check access.

References

  1. 1.

    M. A. Krasnosel’skii and A. V. Pokrovskii, Systems with Hysteresis [in Russian], Nauka, Moscow (1983).

  2. 2.

    R. E. Kalman, R. L. Falb, and M. A. Arbib, Topics in Mathematical System Theory, McGraw-Hill, New York (1969).

  3. 3.

    M. A. Krasnosel’skii and A. V. Pokrovskii, “Vibrostability of solutions of differential equations,” Dokl. Akad. Nauk SSSR, 195, No. 3, 544–547 (1970).

  4. 4.

    M. A. Krasnosel’skii and V. V. Chernorutskii, “On one class of hysteresis nonlinearities,” Dokl. Akad. Nauk SSSR, 305, No. 5, 1065–1069 (1989).

  5. 5.

    V. V. Chernorutskii and M. A. Krasnosel’skii, “Hysteresis systems with variable characteristics,” Nonlin. Anal. Theor., Meth. Appl., 18, No. 6, 543–557 (1992).

  6. 6.

    V. K. Dzyadyk, Introduction to the Theory of Uniform Approximation of Functions by Polynomials [in Russian], Nauka, Moscow (1977).

  7. 7.

    V. I. Borzdyko, Differential Equations with Complex Nonlinearities [in Russian], Doctoral-Degree Thesis (Physics and Mathematics), Dushanbe (2000).

  8. 8.

    G. M. Fikhtengol’ts, A Course in Differential and Integral Calculus [in Russian], Vol. 1, Nauka, Moscow (1960).

  9. 9.

    V. I. Borzdyko, “Variable hysteron,” Dokl. Ros. Akad. Nauk, 324, No. 2, 269–272 (1992).

  10. 10.

    V. I. Borzdyko, “Nonlinear nonstationary systems with hysteresis,” Avtomat. Telemekh., No. 5, 20–26 (1994).

  11. 11.

    V. I. Borzdyko, “Variable hysteron,” in: Abstr. of the Scientific School-Seminar “Simulation and Investigation of Physical Processes” [in Russian], (Kiev, May 1991), p. 9.

Download references

Author information

Correspondence to V. I. Borzdyko.

Additional information

__________

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 3, pp. 295–309, March, 2008.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Borzdyko, V.I. Hysteresis nonstationary nonlinearities. Ukr Math J 60, 339–356 (2008). https://doi.org/10.1007/s11253-008-0062-3

Download citation

Keywords

  • Lipschitz Condition
  • Nonnegative Number
  • Continuous Input
  • Input Satis
  • Complex Nonlinearity