Skip to main content
SpringerLink
Log in

On the Coordinate Synchronization Problem for Dynamical Systems

  • Published:
Differential Equations 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

REFERENCES

  1. Huygens, C., Horologium oscillatorium, Paris, 1673.

  2. Blekhman, I.I., Sinkhronizatsiya dinamicheskikh sistem(Synchronization of Dynamical Systems), Moscow, 1971.

  3. Blekhman, I.I., Synchronization in Science and Technology, New York, 1988.

  4. Cuomo, K., Oppenheim, A., and Strogatz, S., Int. J. Bifurc. Chaos, 1993, vol. 3, pp. 1629–1638.

    Google Scholar 

  5. Blekhman, I.I., Landa, P.S., and Rosenblum, M.G., Appl. Mech. Rev., part 1, 1995, vol. 48, no. 11, pp. 733–752.

    Google Scholar 

  6. Blekhman, I.I., Fradkov, A.L., Nijmeijer, H., and Pogromsky, A.Yu., Systems and Control Letters, 1997, vol. 31, pp. 299–305.

    Google Scholar 

  7. Pecora, L.M. and Carroll, T.L., Phys. Rev. Lett., 1990, vol. 64, no. 8, pp. 821–824.

    Google Scholar 

  8. Lyapunov, A.M., Sobr. soch.(Collected Works), Moscow, 1956, vol. 2.

  9. Rumyantsev, V.V., Vestn. MGU. Matematika, Mekhanika, Fizika, Astronomiya, Khimiya, 1957, no. 4, pp. 9–16.

    Google Scholar 

  10. Zubov, V.I., Matematicheskie metody issledovaniya sistem avtomaticheskogo regulirovaniya(Mathematical Methods for Investigation of Control Systems), Leningrad, 1959.

  11. Corduneanu, C., Rev. Roum. Math. Pure et Appl., 1964, vol. 9, no. 3, pp. 229–236.

    Google Scholar 

  12. Matrosov, V.M., Trudy II Vsesoyuz. s'ezda po teoret. i prikl. mekhanike(Proc. II All-Union Conf. on Theor. and Appl. Mechanics), Moscow, 1965, pp. 112-115.

  13. Halanay, A., Differential Equations: Stability, Oscillations, Time Lags, New York, 1966.

  14. Peiffer, K. and Rouche, N., J. Mec., 1969, vol. 8, no. 2, pp. 323–334.

    Google Scholar 

  15. Risito, S., Ann. Math. Pura Appl., 1970, vol. 84, pp. 279–292.

    Google Scholar 

  16. Khapaev, M.M., Usrednenie v teorii ustoichivosti(Averaging in Stability Theory), Moscow, 1986.

  17. Rumyantsev, V.V. and Oziraner, A.S., Ustoichivost' i stabilizatsiya dvizheniya po otnosheniyu k chasti peremennykh(Stability and Stabilization of Motion with Respect to Part of the Variables), Moscow, 1987.

  18. Savchenko, A.Ya. and Ignat'ev, A.O., Nekotorye zadachi ustoichivosti neavtonomnykh sistem(Some Problems in the Stability of Nonautonomous Dynamical Systems), Kiev, 1989.

  19. Hatvani, L., Alkalmaz. Mat. Lapok., 1990/1991, vol. 15, no. 1/2, pp. 1–90.

    Google Scholar 

  20. Andreev, A.S., Prikl. Mat. Mekh., 1991, vol. 54, no. 4, pp. 539–547.

    Google Scholar 

  21. Vorotnikov, V.I., Ustoichivost' dinamicheskikh sistem po otnosheniyu k chasti peremennykh(Stability of Dynamical Systems with Respect to Some of the Variables), Moscow, 1991.

  22. Vorotnikov, V.I., Avtomat. Telemekh., 1993, no. 3, pp. 3–62.

    Google Scholar 

  23. Vorotnikov, V.I., Partial Stability and Control, Boston etc., 1998.

  24. Fradkov, A.L., Miroshnik, I.V., and Nikiforov, V.O., Nonlinear and Adaptive Control of Complex Systems, Dordrecht, 1999.

  25. Vorotnikov, V.I. and Rumyantsev, V.V., Ustoichivost' i upravlenie po chasti koordinat fazovogo vektora dinamicheskikh sistem: teoriya, metody i prilozheniya(Stability and Control with Respect to Some of the Coordinates of the Phase Vector of Dynamical Systems: Theory, Methods, and Applications), Moscow, 2001.

  26. Vorotnikov, V.I., Dokl. RAN, 2002, vol. 384, no. 1, pp. 47–51.

    Google Scholar 

  27. Vorotnikov, V.I., Prikl. Mat. Mekh., 1995, vol. 59, no. 4, pp. 553–561.

    Google Scholar 

  28. Vorotnikov, V.I., Prikl. Mat. Mekh., 1999, vol. 63, no. 5, pp. 736–745.

    Google Scholar 

  29. Salvadori, L., Ann. Soc. Sci. Bruxelles Ser. I, 1974, vol. 88, no. 2, pp. 183–194.

    Google Scholar 

  30. Marachkov, V.P., Izv. Fiz.-Mat. Obshch. i NII Matematiki i Mekhaniki pri Kazanskom Univ. Ser. 3, 1940, vol. 12, pp. 171–174.

    Google Scholar 

  31. Yoshizawa, T., Stability Theory by Liapunov's Second Method, Tokyo, 1966.

  32. Hahn, W., Stability of Motion, Berlin etc., 1967.

  33. Wu, C.W. and Chua, L.O., Int. J. Bifurc. Chaos, 1994, vol. 4, no. 4, pp. 979–998.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Nizhni Tagil Technological Institute, Ural State Technical University, Nizhni Tagil, Russia

    V. I. Vorotnikov

Authors
  1. V. I. Vorotnikov
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vorotnikov, V.I. On the Coordinate Synchronization Problem for Dynamical Systems. Differential Equations 40, 14–22 (2004). https://doi.org/10.1023/B:DIEQ.0000028709.33842.43

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:DIEQ.0000028709.33842.43

Keywords

Search

Navigation