Skip to main content
SpringerLink
Log in

Frequency-domain criteria for global stability of dynamic systems with the Prandtl and play operators

  • Mechanics
  • Published:
Doklady Physics Aims and scope Submit manuscript

Abstract

The frequency criterion of the global stability of dynamic systems with the Prandtl and “play” operator is formulated. The scheme of its proof is given. The advantage of the criterion obtained as compared with the known Logemann–Ryan criterion is shown.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. L. Prandtl, Zeitschrift für Angewandte Mathematik und Mechanik 8 (2), 85 (1928).

    Article  ADS  Google Scholar 

  2. A. A. Andronov and N. N. Bautin, Dokl. Akad. Nauk SSSR 46 (7), 304 (1945).

    Google Scholar 

  3. A. Visintin, Differential Models of Hysteresis (Springer, N.Y., 1994).

    Book  MATH  Google Scholar 

  4. M. Brokate and J. Sprekels, Hysteresis and Phase Transitions (Springer, N.Y., 1996).

    Book  MATH  Google Scholar 

  5. A. Visintin, in The Science of Hysteresis (Elsevier, Amsterdam, 2006).

    MATH  Google Scholar 

  6. M. A. Krasnosel’skii and A. V. Pokrovskii, Systems with Hysteresis (Nauka, Moscow, 1983).

    MATH  Google Scholar 

  7. V. A. Yakubovich, in Methods of Investigation of Nonlinear Automatic Control Systems (Nauka, Moscow, 1975).

    Google Scholar 

  8. G. A. Leonov, I. M. Burkin, and A. I. Shepeljavyi, Frequency Methods in Oscillation Theory (Kluwer, Dordrecht, 1996).

    Book  MATH  Google Scholar 

  9. V. A. Yakubovich, Dokl. Akad. Nauk SSSR 149 (2), 288 (1963).

    MathSciNet  Google Scholar 

  10. V. A. Yakubovich, Avtom. Telemekh. 26 (5), 753 (1965).

    Google Scholar 

  11. V. A. Yakubovich, Avtom. Telemekh. No. 12, 51 (1975).

    Google Scholar 

  12. N. E. Barabanov and V. A. Yakubovich, Avtom. Telemekh., No. 12, 5 (1979).

    Google Scholar 

  13. H. Logemann and E. P. Ryan, ESAIM:COCV 9, 169 (2003).

    Article  Google Scholar 

  14. H. Logemann and A. D. Mawby, in Advances in Mathematical Systems Theory (Birkhäuser, Boston, 2001).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, 199034, Russia

    G. A. Leonov & K. D. Aleksandrov

Authors
  1. G. A. Leonov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. D. Aleksandrov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. A. Leonov.

Additional information

Original Russian Text © G.A. Leonov, K.D. Aleksandrov, 2017, published in Doklady Akademii Nauk, 2017, Vol. 477, No. 6, pp. 657–659.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Leonov, G.A., Aleksandrov, K.D. Frequency-domain criteria for global stability of dynamic systems with the Prandtl and play operators. Dokl. Phys. 62, 564–566 (2017). https://doi.org/10.1134/S1028335817120084

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1028335817120084

Search

Navigation