Skip to main content
SpringerLink
Log in

Robust stabilization of uncertain linear dynamical systems with time-varying delay

  • Contributed Papers
  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

In this paper, the problem of the robust stabilization for a class of uncertain linear dynamical systems with time-varying delay is considered. By making use of an algebraic Riccati equation, we derive some sufficient conditions for robust stability of time-varying delay dynamical systems with unstructured or structured uncertainties. In our approach, the only restriction on the delay functionh(t) is the knowledge of its upper boundh −. Some analytical methods are employed to investigate these stability conditions. Since these conditions are independent of the delay, our results are also applicable to systems with perturbed time delay. Finally, a numerical example is given to illustrate the use of the sufficient conditions developed in this paper.

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

Similar content being viewed by others

References

  1. Kwon, W. H., andPearson, A. E.,Feedback Stabilization of Linear Systems with Delay Control, IEEE Transactions on Automatic Control, Vol. 25, pp. 266–269, 1980.

    Google Scholar 

  2. Patel, N. K., Das, P. C., andPrabhu, S. S.,Optimal Control of Systems Described by Delay Differential Equations, International Journal of Control, Vol. 36, pp. 303–311, 1982.

    Google Scholar 

  3. Wu, W. T., Chu, Y. T., andHopper, J. R.,A Method for Control of Time Delay Systems, International Journal of Control, Vol. 38, pp. 211–220, 1983.

    Google Scholar 

  4. Alford, R. L., andLee, E. B.,Sampled Data Hereditary Systems: Linear Quadratic Theory, IEEE Transactions on Automatic Control, Vol. 31, pp. 60–65, 1986.

    Google Scholar 

  5. Watanabe, K., Ito, M., Kaneko, M., andOuchi, T.,Finite Spectrum Assignment Problem for Systems with Delay in State Variable, IEEE Transactions on Automatic Control, Vol. 28, pp. 506–508, 1983.

    Google Scholar 

  6. Watanabe, K., Ito, M., Kaneko, M., andOuchi, T.,Finite Spectrum Assignment Problem of Systems with Multiple Commensurate Delay in State and Control, International Journal of Control, Vol. 39, pp. 1073–1082, 1984.

    Google Scholar 

  7. Thowsen, A.,Stabilization of a Class of Linear Time-Delay Systems, International Journal of Systems Science, Vol. 12, pp. 1485–1492, 1981.

    Google Scholar 

  8. Thowsen, A.,Stable Sampled-Data Feedback Control of Dynamic Systems with Time Delay, International Journal of Systems Science, Vol. 13, pp. 1379–1384, 1982.

    Google Scholar 

  9. Feliachi, A., andThowsen, A.,Memoryless Stabilization of Linear Delay-Differential Systems, IEEE Transactions on Automatic Control, Vol. 26, pp. 586–587, 1981.

    Google Scholar 

  10. Mori, T., Noldus, E., andKuwahara, M.,A Way to Stabilize Linear Systems with Delayed State, Automatica, Vol. 19, pp. 571–573, 1983.

    Google Scholar 

  11. Noldus, N.,Stabilization of a Class of Distributional Convolution Equations, International Journal of Control, Vol. 41, pp. 947–960, 1985.

    Google Scholar 

  12. Ikeda, I., andAshida, T.,Stabilization of Linear Systems with Time-Varying Delay, IEEE Transactions on Automatic Control, Vol. 24, pp. 369–370, 1979.

    Google Scholar 

  13. Lee, T. N., andDianat, S.,Stability of Time-Delay Systems, IEEE Transactions on Automatic Control, Vol. 26, pp. 951–953, 1981.

    Google Scholar 

  14. Su, T. J., Fong, I. K., Kuo, T. S., andSun, Y. Y.,Robust Stability for Linear Time-Delay Systems with Linear Parameter Perturbation, International Journal of Systems Science, Vol. 19, pp. 2123–2129, 1988.

    Google Scholar 

  15. Wang, S. S., andLin, T. P.,Robust Stabilization of Uncertain Time-Delay Systems with Sampled Feedback, International Journal of Systems Science, Vol. 19, pp. 399–401, 1988.

    Google Scholar 

  16. Chou, J. H., Horng, I. R., andChen, B. S.,Dynamical Feedback Compensator for Uncertain Time-Delay Systems Containing Saturating Actuators, International Journal of Control, Vol. 49, pp. 961–968, 1989.

    Google Scholar 

  17. Wu, H. S., Willgoss, R. A., andMizukami, K.,Robust Stabilization for a Class of Uncertain Dynamical Systems with Time Delay, Journal of Optimization Theory and Applications, Vol. 82, pp. 361–377, 1994.

    Google Scholar 

  18. Sinha, A. S. C.,Stabilization of Large-Scale Nonlinear Infinite-Delay Systems, International Journal of Systems Science, Vol. 21, pp. 2679–2684, 1990.

    Google Scholar 

  19. Franklin, J. N.,Matrix Theory, Prentice-Hall, Englewood Cliffs, New Jersey, 1968.

    Google Scholar 

  20. Patel, R. V., Toda, M., andSridhar, B.,Robustness of Linear-Quadratic State Feedback Designs in the Presence of System Uncertainty, IEEE Transactions on Automatic Control, Vol. 22, pp. 945–949, 1977.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Division of Mathematical and Information Sciences, Faculty of Integrated Arts and Sciences, Hiroshima University, Higashi-Hiroshima City, Japan

    H. S. Wu (Associate Professor) & K. Mizukami (Professor)

Authors
  1. H. S. Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. Mizukami
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by G. Leitmann

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wu, H.S., Mizukami, K. Robust stabilization of uncertain linear dynamical systems with time-varying delay. J Optim Theory Appl 82, 593–606 (1994). https://doi.org/10.1007/BF02192220

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02192220

Key Words

Search

Navigation