Skip to main content
Log in

Relative Controllability in Systems with Pure Delay

  • Published:
International Applied Mechanics Aims and scope

Abstract

A linear control system with pure delay is considered. The integral-form solution of the Cauchy problem is obtained. The relative-controllability problem and the stabilization problem for a pendulum with time delay are solved

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. N. V. Azbelev, V. P. Maksimov, and L. F. Rakhmatullina, An Introduction to the Theory of Functional Differential Equations [in Russian], Nauka, Moscow (1991).

    Google Scholar 

  2. M. Athans and P. L. Falb, Optimal Control, McGraw Hill, New York (1966).

    Google Scholar 

  3. V. N. Afanas’ev, V. B. Kolmanovskii, and V. R. Nosov, Mathematical Theory of Control System Design [in Russian], Vyssh. Shkola, Moscow (1989).

    Google Scholar 

  4. R. Gabasov and F. M. Kirillova, Qualitative Theory of Optimal Processes [in Russian], Nauka, Moscow (1971).

    Google Scholar 

  5. F. R. Gantmakher, Theory of Matrices [in Russian], Nauka, Moscow (1988).

    Google Scholar 

  6. B. M. Zhirnov, “The Thomson friction self-oscillations of a two-mass system with delay,” Int. Appl. Mech., 36, No.7, 969–977 (2000).

    Google Scholar 

  7. B. M. Zhirnov, “Forced quasilinear resonant vibrations of a frictional mechanical system with delay, ” Int. Appl. Mech., 38, No.4, 507–512 (2002).

    Article  Google Scholar 

  8. R. Kalman, P. Falb, and M. Arbib, Topics in Mathematical System Theory, McGraw-Hill, New York (1969).

    Google Scholar 

  9. F. M. Kirillova and S. V. Churakova, “The controllability problem for linear systems with aftereffect, ” Diff. Uravn., 3, No.3, 436–445 (1967).

    Google Scholar 

  10. V. Lakshmikantham and A. A. Martynyuk, “Development of the direct Lyapunov method for delay systems (survey),” Int. Appl. Mech., 29, No.2, 83–96 (1993).

    Article  Google Scholar 

  11. V. B. Larin, “Control problems for systems with uncertainty,” Int. Appl. Mech., 37, No.12, 1539–1567 (2001).

    Article  Google Scholar 

  12. L. L. Lobas, “Influence of an asymmetric follower force on the stationary states of a double-link pendulum,” Int. Appl. Mech., 37, No.12, 1618–1623 (2001).

    Article  MathSciNet  Google Scholar 

  13. A. A. Martynyuk and N. V. Nikitina, “The theory of motion of a double mathematical pendulum,” Int. Appl. Mech., 36, No.9, 1252–1258 (2000).

    Article  Google Scholar 

  14. A. A. Martynyuk and N. V. Nikitina, “Regular and chaotic motions of mathematical pendulums,” Int. Appl. Mech., 37, No.3, 407–413 (2001).

    Article  Google Scholar 

  15. A. A. Martynyuk and A. Rizaev, “Sufficient stability conditions for systems with delay,” Int. Appl. Mech., 37, No.12, 1612–1617 (2001).

    Article  Google Scholar 

  16. J. Hale, Theory of Functional Differential Equations, Springer-Verlag, New York-Heidelberg-Berlin (1977).

    Google Scholar 

  17. L. E. Elsgol’ts and S. B. Norkin, An Introduction to the Theory of Delay Differential Equations [in Russian], Nauka, Moscow (1971).

    Google Scholar 

  18. V. V. Koval’chuk and V. L. Lobas, “Divergent bifurcations of a double pendulum under the action of an asymmetric follower force,” Int. Appl. Mech., 40, No.7, 821–828 (2004).

    Article  Google Scholar 

  19. A. A. Martynyuk and V. G. Miladzhanov, “Stability of singularly perturbed systems with structural perturbations. Some applications,” Int. Appl. Mech., 39, No.8, 875–894 (2003).

    Article  Google Scholar 

  20. A. A. Martynyuk and V. I. Slyn’ko, “Stability of a nonlinear impulsive system,” Int. Appl. Mech., 40, No.2, 231–239 (2004).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

__________

Translated from Prikladnaya Mekhanika, Vol. 41, No. 2, pp. 118–130, February 2005.

The study was partially sponsored by the State Committee of Science and Technology of Ukraine (grant No. 01. 07/00081).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Khusainov, D.Y., Shuklin, G.V. Relative Controllability in Systems with Pure Delay. Int Appl Mech 41, 210–221 (2005). https://doi.org/10.1007/s10778-005-0079-3

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10778-005-0079-3

Keywords

Navigation