Skip to main content
Log in

Dynamic properties of automatic control systems: Investigation via order reduction

  • Determinate Systems
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

Recurrent methods are applied to study the stability of automatic control systems in the first linear approximation. These methods are not analytic in general sense, but, in performance, accuracy, and practical realization, supplement the well-known Routh-Hurwitz, Mikhailov, Jury, Pontryagin, Neimark, and Barabanov analytical criteria and recurrent algorithms and similar criteria in this field.

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.

Similar content being viewed by others

REFERENCES

  1. Polyak, B.T. and Shcherbakov, P.S., Robastnaya ustoichivost’ i upravlenie (Robust Stability and Control), Moscow: Nauka, 2002.

    Google Scholar 

  2. Mikhailov, A.V., Harmonic Analysis Methods in Control Theory, Avtom. Telemekh., 1938, vol. 3, pp. 27–81.

    Google Scholar 

  3. Jury, E.I., Innors and Stability of Dynamic Systems, New York: Wiley, 1974. Translated under the title Innory i ustoichivost’ dinamicheskikh sistem, Moscow: Nauka, 1979.

    Google Scholar 

  4. Pontryagin, L.S., Zeros of Certain Elementary Transcendental Functions, Izv. Akad. Nauk SSSR, Mat., 1942, vol. 6, pp. 27–81.

    Google Scholar 

  5. Neimark, Yu. I., Dinamicheskie sistemy i upravlyaemye protsessy (Dynamic Systems and Control Processes), Moscow: Nauka, 1978.

    Google Scholar 

  6. Barabanov, A.T., Complete Solution of the Routh Problem in Control Theory, Dokl. Akad. Nauk SSSR, 1988, vol. 301, no. 5, pp. 1061–1065.

    Google Scholar 

  7. Postnikov, M.M., Ustoichivye mnogochleny (Stable Polynomials), Moscow: Nauka, 1981.

    Google Scholar 

  8. Blistanova, L.D., Zubov, I.V., Zubov, N.V., and Severtsev, N.A., Konstruktivnye metody teorii ustoichivosti i ikh primenenie k zadacham chislennogo analiza (Constructive Methods of Stability Theory and Their Application to Problems of Numerical Analysis), St. Petersburg: S.-Peterburg. Gos. Univ., 2002.

    Google Scholar 

  9. Lobachevsky, N.I., Polnoe sobranie sochinenii (Complete Collection of Works), Moscow: Gostekhizdat, vol. 4, 1948.

    Google Scholar 

  10. Kurosh, A.G., Kurs vysshei algebry (A Course in Higher Algebra), Moscow: Nauka, 1971.

    Google Scholar 

  11. Kharitonov, V.L., Asymptotic Stability of a Family of Systems of Linear Differential Equations, Diff Uravn., 1978, vol. 14, no. 11, pp. 2086–2088.

    Google Scholar 

  12. Chebyshev, P.L., Vysshaya algebra (Higher Algebra), Moscow: Akad. Nauk SSSR, 1936.

    Google Scholar 

  13. Prasolov, V.V., Mnogochleny (Polynomials), Moscow: MTsNMO, 2001.

    Google Scholar 

  14. Demidovich, B.P., Lektsii po matematicheskoi teorii ustoichivosti (Lectures on Mathematical Theory of Stability), Moscow: Mosk. Gos. Univ., 1998.

    Google Scholar 

  15. Blistanova, L.D. and Zubov, N.V., Recursive Algorithms for Investigating the Stability of Linear Stationary Systems, Proc. VI Int. Workshop Beam Dynamics and Optimization, St. Petersburg, 2003, pp. 75–85.

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Avtomatika i Telemekhanika, No. 2, 2005, pp. 17–22.

Original Russian Text Copyright © 2005 by Blistanova, I. Zubov, N. Zubov, Severtsev.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Blistanova, L.D., Zubov, I.V., Zubov, N.V. et al. Dynamic properties of automatic control systems: Investigation via order reduction. Autom Remote Control 66, 184–188 (2005). https://doi.org/10.1007/s10513-005-0042-0

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10513-005-0042-0

Keywords

Navigation