Advertisement

Stabilization of linear discrete-time systems with saturating controls and norm-bounded time-varying uncertainty

  • Sophie Tarbouriech
  • Germain Garcia
Chapter
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 227)

Keywords

Global Stabilization Uncertain System Symmetric Positive Definite Matrix Quadratic Lyapunov Function Quadratic Stabilizability 
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.
    J. Alvarez-Ramirez, R. Suarez, J. alvarez: Semi-global stabilization of multi-input linear systems with saturated linear state feedback, Systems & Control Letters, 23, pp.247–254, 1994.Google Scholar
  2. 2.
    J.P. Aubin and A. Cellina: Differential inclusions, Springe-Verlag, 1984.Google Scholar
  3. 3.
    B.R. Barmish: Necessary and sufficient conditions for quadratic stabilizability of an uncertain system, J. Optim. Theory Appl., vol.46, no.4, pp., 1985.Google Scholar
  4. 4.
    D.S. Bernstein and A.N. Michel: A chronological bibliography on saturating actuators, Int. J. of Robust and Nonlinear Control, vol.5, pp.375–380, 1995.Google Scholar
  5. 5.
    C. Burgat and S. Tarbouriech: Non-Linear Systems, vol.2, Chapter 4, Annexes C, D, E, Chapman & Hall, London (U.K), 1996.Google Scholar
  6. 6.
    P. Dorato: Robust Control, IEEE Press Book, 1987.Google Scholar
  7. 7.
    G. Garcia, J. Bernussou, D. Arzelier: Robust stabilization of discrete-time linear systems with norm-bounded time varying uncertainty, Systems and Control Letters, vol.22, pp.327–339, 1994.CrossRefGoogle Scholar
  8. 8.
    G. Garcia, J. Bernussou, D. Arzelier: Disk pole location control for uncertain system with H 2 guaranteed cost, LAAS Report no.94216, submitted for review.Google Scholar
  9. 9.
    Z. Lin and A. Saberi: Semi-global exponential stabilization of linear discrete-time systems subject to input saturation via linear feedbacks, Systems and Control Letters, 24, pp.125–132, 1995.CrossRefGoogle Scholar
  10. 10.
    C.C.H. Ma: Unstability of linear unstable systems with inputs limits, J. of Dynamic Syst., Measurement and Control, 113, pp.742–744, 1991.Google Scholar
  11. 11.
    A.P. Molchanov and E.S. Pyatniskii: Criteria of asymptotic stability of differential and difference inclusions encountered in control theory, Systems and Control Letters, 13, pp.59–64, 1989.CrossRefGoogle Scholar
  12. 12.
    R. Suarez, J. Alvarez-Ramirez, J. Alvarez: Linear systems with single saturated input: stability analysis, Proc. of 30th IEEE-CDC, Brighton, England, pp.223–228, December 1991.Google Scholar
  13. 13.
    S. Tarbouriech and G. Garcia: Global stabilization for linear discrete-time systems with saturating controls and norm-bounded time-varying uncertainty, LAAS Report no.95112, submitted for review.Google Scholar
  14. 14.
    G.F. Wredenhagen and P.R. Bélanger: Piecewise-linear LQ control for systems with input constraints, Automatica, vol.30, no.3, pp.403–416, 1994.CrossRefGoogle Scholar
  15. 15.
    Y. Yang: Global stabilization of linear systems with bounded feedback, Ph.D. Dissertation, New Brunswick Rutgers, the State University of New Jersey, 1993.Google Scholar
  16. 16.
    K. Yoshida and H. Kawabe: A design of saturating control with a guaranteed cost and its application to the crane control system, IEEE Trans. Autom. Control, vol.37, no.1, pp.121–127, 1992.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 1997

Authors and Affiliations

  • Sophie Tarbouriech
    • 1
  • Germain Garcia
    • 1
  1. 1.L.A.A.S. — C.N.R.S.Toulouse cedex 4France

Personalised recommendations