Skip to main content
Log in

Frequency-domain criteria for oscillation in nonlinear systems with one stationary nonlinear component

  • 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

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

Instant access to the full article PDF.

Literature Cited

  1. A. M. Letov, Stability of Nonlinear Control Systems [in Russian], Gostekhizdat, Moscow (1962).

    Google Scholar 

  2. M. A. Aizerman and F. R. Gantmakher, Absolute Stability of Nonlinear Controlled Systems [in Russian], Izd-vo AN SSSR, Moscow (1963).

    Google Scholar 

  3. S. Lefshets, Stability of Nonlinear Automatic Control Systems [in Russian], Mir, Moscow (1967).

    Google Scholar 

  4. A. F. Filippov, “Differential equations with a discontinuous right side,” Matem. Sbornik, 51 (93), No. 1, 99–128 (1960).

    Google Scholar 

  5. V. A. Yakubovich, “Absolute stability of nonlinear controlled systems in critical cases, III,” Avtomat. i Telemekhan.,25, No. 5, 601–612 (1964).

    Google Scholar 

  6. V. S. Georgievskii, M. V. Levit and V. A. Yakubovich, “Frequency-domain criteria for oscillation in nonlinear controlled systems,” Avtomat. i Telemekhan., No. 2, 30–39 (1972).

    Google Scholar 

  7. V. A. Yakubovich, “Frequency-domain criteria for absolute stability of nonlinear automatic control systems,” Proceedings of the Inter-Collegiate Conference on Applied Theory of Stability and Analytic Mechanics, Kazan', 1962, Izd-vo KAN (1965), pp. 135–141.

  8. H. B. L. Brockett, “Frequency domain instability criteria for time-varying and nonlinear systems,” Proc. IEEE,55, No. 5, 604–619 (1967).

    Google Scholar 

  9. V. A. Yakubovich, “Absolute instability of nonlinear control systems, I. General frequency-domain criteria,” Avtomat. i Telemekhan., No. 12, 5–12 (1970).

    Google Scholar 

  10. V. A. Yakubovich, “The S-procedure in nonlinear control theory,” Vestn. Leningr. Un-ta, No. 1, 62–77 (1971).

    Google Scholar 

  11. V. A. Yakubovich, “A frequency theorem in control theory,” Sibirsk. Matem. Zh.,14, No. 2, 384–420 (1973).

    Google Scholar 

  12. V. A. Yakubovich, “Solution of some matrix inequalities encountered in automatic control theory,” Dokl. AN SSSR,143, No. 6, 1304–1307 (1962).

    Google Scholar 

  13. V. A. Yakubovich, “Absolute instability of nonlinear control systems, II. Systems with nonstationary nonlinear units. The circle criterion,” Avtomat. i Telemekhan., No. 6, 25–34 (1971).

    Google Scholar 

  14. E. N. Barabashin and N. N. Krasovskii, “On the stability on motion on the whole,” Dokl. AN SSSR,76, No. 3, 453–456 (1962).

    Google Scholar 

  15. V. A. Yakubovich, “Method of matrix inequalities in theory of stability of nonlinear controlled systems,” Avotmat. i Telemekhan.,25, No. 7, 1017–1029 (1964).

    Google Scholar 

  16. V. A. Yakubovich, “Stability on the whole of undisturbed motion for equations of indirect automatic control,” Vestn. Leningr. Un-ta, No. 19, 172–175 (1957).

    Google Scholar 

  17. P. Hartman, Ordinary Differential Equations, Wiley (1964).

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

    Google Scholar 

  19. F. R. Gantmakher, Theory of Matrices [in Russian], Nauka, Moscow (1967).

    Google Scholar 

Download references

Authors

Additional information

Translated from Sibirskii Matematicheskii Zhurnal, Vol. 14, No. 5, pp. 1100–1129, September–October, 1973.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yakubovich, V.A. Frequency-domain criteria for oscillation in nonlinear systems with one stationary nonlinear component. Sib Math J 14, 768–788 (1973). https://doi.org/10.1007/BF00969914

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00969914

Keywords

Navigation