Advertisement

Dynamics and Control

, Volume 4, Issue 2, pp 147–167 | Cite as

A method for designing a stabilizing control for a class of uncertain linear delay systems

  • Takashi Amemiya
  • George Leitmann
Article

Abstract

We present a simple method for designing stabilizing controllers for linear delay equations containing unmatched uncertainty. The methodology employed is based on differential inequalities rather than on Lyapunov stability theory.

Keywords

Stability Theory Delay System Lyapunov Stability Differential Inequality Delay Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    G. Leitmann, “On the efficacy of nonlinear control in uncertain linear systems”J. of Dynam. Syst., Meas., Contr., vol. 102, no. 6, 1981.Google Scholar
  2. 2.
    B. R. Barmish and G. Leitmann, “On ultimate boundedness control of uncertain systems in the absence of matching assumptions”,IEEE Trans. on Automat. Contr., vol. AC-27 no. 1, Feb. 1982.Google Scholar
  3. 3.
    T. Amemiya, “On the global asymptotic stability of off-diagonally monotone dynamical systems”,IEEE Trans. CAS, vol. 114, no. 12, 1985.Google Scholar
  4. 4.
    T. Amemiya, “Stability analysis of nonlinearly interconnected systems-application of M-functions”,J. Math. Anal. Appl., vol. 114, no. 1, 1986.Google Scholar
  5. 5.
    K. Akazawa, T. Amemiya, and H. Tokumaru, “Further conditions for the delay-independent stabilization of linear systems”,Int. J. of Contr., vol. 46, no. 4, 1987.Google Scholar
  6. 6.
    T. Amemiya, K. Akazawa, and H. Tokumaru, “Delay-independent stabilization and decay rate assignability of linear systems with limited measurable state variables”,Int. J. of Contr., vol. 47, no. 1, 1988.Google Scholar
  7. 7.
    T. Amemiya, “Delay-independent stability of higher-order systems”,Int. J. of Contr., vol. 50, no. 1, 1989.Google Scholar
  8. 8.
    G. Leitmann and S. Pandey, “A controller for a class of mismatched uncertain systems”Proc. 28th IEEE CDC, 1989.Google Scholar
  9. 9.
    G. Leitmann and S. Pandey, “Aircraft control under conditions of windshear”,Contr. and Dynam. Syst., vol. 24, (ed. by G.T. Leondes), Academic Press, 1989.Google Scholar
  10. 10.
    C. S. Lee and G. Leitmann, “Continuous feedback guaranteeing uniform ultimate boundedness for uncertain linear delay systems: An application to river pollution control”,Comput. Math. Applic., vol 16, no. 10/11, 1988.Google Scholar
  11. 11.
    A. Thowsen, “Uniform ultimate boundedness of the solutions of uncertain dynamic delay systems with state-dependent and memoryless feedback control”,Int. J. of Contr., vol. 37, no. 5, 1983.Google Scholar
  12. 12.
    H. Tokumaru, N. Adachi, and T. Amemiya, “Macroscopic stability of interconnected systems”,Preprint of 6th IFAC Congress, no. 44.4, 1975.Google Scholar
  13. 13.
    N. N. Krasovkii,Stability of Motion. Stanford Univ. Press, 1963.Google Scholar
  14. 14.
    V. Lakshmikantham and S. Leera,Differential and Integral Inequalities. Academic Press, 1969.Google Scholar
  15. 15.
    A. Haranay,Differential Equations. Academic Press, 1966.Google Scholar
  16. 16.
    J.M. Ortega and W.C. Rheinboldt,Iterative Solution of Nonlinear Equations in Several Variables. Academic Press, 1970.Google Scholar
  17. 17.
    Y. Yu, “On stabilizing uncertain delay systems”,J. Optim. Theory Appl., vol. 41, no 3, 1983.Google Scholar
  18. 18.
    E. Cheres, S. Gutman, and Z.I. Palmor, “Stabilization of uncertain dynamic systems including state delays”,IEEE Trans. on Automat. Contr. vol. AC-34, no. 11, 1989.Google Scholar
  19. 19.
    K. Weis, “Audratic stability of linear systems with structural independent time-varying uncertainties”,IEEE Trans. on Automat. Contr., vol. 35, no. 3, 1990.Google Scholar

Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Takashi Amemiya
    • 1
  • George Leitmann
    • 2
  1. 1.Tokyo Metropolitan Institute of TechnologyHino, TokyoJapan
  2. 2.Department of Mechanical EngineeringUniversity of California, BerkeleyBerkeleyUSA

Personalised recommendations