Skip to main content
SpringerLink
Log in

On the boundedness of the trajectories of phase systems

  • Notes
  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

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

Literature Cited

  1. E. A. Barbashin and V. A. Tabueva, Dynamical Systems with a Cylindrical Phase Space [in Russian], Nauka, Moscow (1969).

    Google Scholar 

  2. V. A. Yakubovich, “Solution of certain matrix inequalities encountered in control theory,” Dokl. Akad. Nauk SSSR,143, No. 7, 1304–1307 (1962).

    Google Scholar 

  3. V. M. Popov, Hyperstability of Control Systems [in Russian], Nauka, Moscow (1970).

    Google Scholar 

  4. Z. S. Batalova, “Rotor motions under an external harmonic force,” Mekhan. Tverd. Tela, No. 2, 66–73 (1967).

    Google Scholar 

  5. A. Moraru, “Nonlinear vibrations during the starting of synchronous machines with a pulsating torque,” in: Applications of the Theory of Nonlinear Oscillations in Electrical Engineering and Electronics, Proceedings of the Fifth International Conference on Nonlinear Oscillations [in Russian], Vol. 4, Izd. AN UkrSSR, Kiev (1970), pp. 367–384.

    Google Scholar 

  6. A. Moraru, “Demarrage et marche du micromoteur synchrone monophasé,” Rev. Scitechn. Electrotechnique et Energetique (Bucarest), No. 4, 549–562 (1967).

    Google Scholar 

  7. G. A. Leonov, “On the stability of phase systems,” Sib. Matem. Zh.,15, No. 1, 49–60 (1974).

    Google Scholar 

  8. E. Noldus, “On the stability of systems having several equilibrium states,” Appl. Sci. Res.,21, No. 3-4, 219–233 (1969).

    Google Scholar 

  9. V. A. Yakubovich, “Absolute stability of nonlinear control systems in critical cases, III.” Avtomat. i Telemekhan., No. 5, 601–612 (1964).

    Google Scholar 

  10. M. V. Kapranov, “The locking band in phase-locked frequency control,” Radiotekhnika, No. 12, 37–52 (1956).

    Google Scholar 

  11. W. J. Gruen, “Theory of AFC synchronization,” Proc. Inst. Radio Engrs.,41, No. 8, 1043–1048 (1953).

    Google Scholar 

  12. L. N. Belyustina, “Study of a nonlinear system of phase-locked frequency control,” Radiofizika,2, No. 2, 277–292 (1959).

    Google Scholar 

  13. T. J. Rey, “Automatic phase control: theory design,” Proc. Inst. Radio Engrs.,48, No. 10, 1760–1771 (1960).

    Google Scholar 

  14. M. Brunk, “Der Fangbereich von Nachlaufsynchronisationschaltung mit Sinusförmiger Charakteristik des Phasendiskriminators,” Arch. der Elektr. Übertrag.,19, No. 12, 649–663 (1965).

    Google Scholar 

  15. N. N. Bautin, “Qualitative study of an equation of the theory of phase-locked frequency control,” Prikl. Matem. i Mekh.,34, No. 5, 850–860 (1970).

    Google Scholar 

  16. Yu. N. Bakaev, “Study of a television synchronization system with lag,” Radiotekhnika i Élektronika, No. 2, 227–236 (1958).

    Google Scholar 

  17. N. A. Gubar', “Study of a piecewise-linear dynamical system with three parameters,” Prikl. Matem. i Mekh.,25, No. 6, 1011–1023 (1961).

    Google Scholar 

  18. B. I. Shakhtarin, “Study of a piecewise-linear system of phase-locked frequency control,” Radiotekhnika i Élektronika, No. 8, 1415–1424 (1969).

    Google Scholar 

Download references

Authors
  1. G. A. Leonov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Sibirskii Matematicheskii Zhurnal, Vol. 15, No. 3, pp 687–692, May–June, 1974.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Leonov, G.A. On the boundedness of the trajectories of phase systems. Sib Math J 15, 491–495 (1974). https://doi.org/10.1007/BF00969820

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00969820

Keywords

Search

Navigation