Skip to main content
Log in

A frequency theorem in control theory

  • 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.

Institutional subscriptions

Literature Cited

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

  2. F. R. Gantmakher and V. A. Yakubovich, “Absolute stability of nonlinear controlled systems,” in: Proceedings of the Second All-Union Session on Theoretical and Applied Mechanics [in Russian], Nauka (1965).

  3. V. A. Yakubovich, “Frequency conditions for the absolute stability of control systems with several nonlinear or linear nonstationary units,” Avtomat. i Telemekhan., No. 6, 5–30 (1967).

    Google Scholar 

  4. V. A. Yakubovich, “Absolute instability of nonlinear control systems, I. General frequency criteria,” Avtomat. i Telemekhan., No. 12, 5–14 (1970).

    Google Scholar 

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

    Google Scholar 

  6. V. A. Yakubovich, “The S-procedure in nonlinear control theory,” Vest. Leningr. Univ., No. 1, 62–77 (1971).

    Google Scholar 

  7. A. M. Letov, “The analytic design of controllers,” Avtomat. i Telemekhan.,21, No. 6, 5–14 (1960).

    Google Scholar 

  8. A. I. Lur'e, Some Nonlinear Problems in Automatic Control Theory [in Russian], Gostekhizdat, Moscow (1951).

    Google Scholar 

  9. V. A. Yakubovich, “The solution of some matrix inequalities encountered in automatic control theory,” Dokl. Akad. Nauk SSSR,143, No. 6, 1304–1306 (1962).

    Google Scholar 

  10. R. E. Kalman, “Liapunov functions for the problem of Lur'e in automatic control,” Proc. Nat. Acad. Sci. USA,49 (1963).

  11. V. M. Popov, “Hyperstability of automatic control systems with several nonlinear elements,” Rev. Roumaine Sci. Techn.,1 (1964).

  12. G. Szegö and R. E. Kalman, “Sur la stabilité absolue d'un systéme d'équations aux différences finies,” C. R. Acad. Sci.,257, 388–390 (1963).

    Google Scholar 

  13. V. A. Yakubovich, “The solution of an algebraic problem encountered in control theory,” Dokl. Akad. Nauk SSSR,193, No. 1, 57–60 (1970).

    Google Scholar 

  14. M. G. Krein and Yu. L. Shmul'yan, “On plus operators in spaces with an indefinite metric,” Matem. Issledovaniya,1, No. 1, 5–61 (1966).

    Google Scholar 

  15. V. A. Yakubovich, “The factoring of symmetric matrix polynomials,” Dokl. Akad. Nauk SSSR,194, No. 3, 532–535 (1970).

    Google Scholar 

Download references

Authors

Additional information

Translated from Sibirskii Matematicheskii Zhurnal, Vol. 14, No. 2, pp. 384–420, March–April, 1973.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yakubovich, V.A. A frequency theorem in control theory. Sib Math J 14, 265–289 (1973). https://doi.org/10.1007/BF00967952

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00967952

Keywords

Navigation