Bounded controllers for robust exponential convergence

  • M. Corless
  • G. Leitmann
Contributed Papers

Abstract

We consider the problem of stabilizing an uncertain system when the norm of the control input is bounded by a prespecified constant. We treat continuous-time dynamical systems whose nominal part is linear and whose uncertain part is norm-bounded by a known affine function of the norm of the system state and the norm of the control input. Given a prespecified rate of convergence and a ball containing the origin of the state space, we present controllers which guarantee that, for all allowable uncertainties and nonlinearities, there is a region of attraction from which all solutions converge to the given ball with the prespecified convergence rate.

Key Words

Robust control bounded control uncertain systems Lyapunov techniques 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Corless, M., andLeitmann, G.,Controller Design for Uncertain Systems via Lyapunov Functions, Proceedings of the American Control Conference, Atlanta, Georgia, pp. 2019–2025, 1988.Google Scholar
  2. 2.
    Corless, M., andLeitmann, G.,Deterministic Control of Uncertain Systems: A Lyapunov Theory Approach, Deterministic Control of Uncertain Systems, Edited by A. Zinober, Peter Peregrinus, London, England, pp. 220–251, 1990.Google Scholar
  3. 3.
    Leitmann, G.,Deterministic Control of Uncertain Systems via a Constructive Use of Lyapunov Stability Theory, System Modelling and Optimization, Edited by H. J. Sebastian and K. Tammer, Lecture Notes in Control and Information Sciences, Springer-Verlag, Berlin, Germany, Vol. 143, pp. 38–55, 1990.Google Scholar
  4. 4.
    Blanchini, F.,Constrained Control for Uncertain Linear Systems, Journal of Optimization Theory and Applications, Vol. 71, pp. 465–484, 1991.Google Scholar
  5. 5.
    Dolphus, R. M., andSchmitendorf, W. E.,Stability Analysis for a Class of Linear Controllers under Control Constraints, Proceedings of the 30th IEEE Conference on Decision and Control, Brighton, England, Vol. 1, pp. 77–80, 1991.Google Scholar
  6. 6.
    Hached, M., Madani-Esfahani, S. M., andZak, S. H.,On the Stability and Estimation of Ultimate Boundedness of Nonlinear/Uncertain Dynamic Systems with Bounded Controllers, Proceedings of the American Control Conference, San Diego, California, Vol. 2, pp. 1180–1185, 1990.Google Scholar
  7. 7.
    Madani-Esfahani, S. M., Hui, S., andZak, S. H.,On the Estimation of Sliding Domains and Stability Regions of Variable Structure Control Systems with Bounded Controllers, Proceedings of the 26th Allerton Conference on Communication, Control, and Computing, Monticello, Illinois, pp. 518–527, 1988.Google Scholar
  8. 8.
    Madani-Esfahani, S. M., andZak, S. H.,Variable Structure Control of Dynamical Systems with Bounded Controllers, Proceedings of the American Control Conference, Minneapolis, Minnesota, Vol. 1, pp. 90–95, 1987.Google Scholar
  9. 9.
    Gutman, P. O., andHagander, P.,A New Design of Constrained Controllers for Linear Systems, IEEE Transactions on Automatic Control, Vol. 30, pp. 22–33, 1985.Google Scholar
  10. 10.
    Soldatos, A. G., andCorless, M.,Stabilizing Uncertain Systems with Bounded Control, Dynamics and Control, Vol. 1, pp. 227–238, 1991.Google Scholar
  11. 11.
    Corless, M.,Guaranteed Rates of Exponential Convergence for Uncertain Systems, Journal of Optimization Theory and Applications, Vol. 64, pp. 481–494, 1990.Google Scholar
  12. 12.
    Swei, S. M., andCorless, M.,On the Necessity of the Matching Condition in Robust Stabilization, Proceedings of the 30th IEEE Conference on Decision and Control, Brighton, England, Vol. 3, pp. 2611–2614, 1991.Google Scholar
  13. 13.
    Petersen, I. R., andHollot, C. V.,A Riccati Equation Approach to the Stabilization of Uncertain Linear Systems, Automatica, Vol. 22, pp. 397–411, 1986.Google Scholar
  14. 14.
    Rotea, M. A., andKhargonekar, P. P.,Stabilization of Uncertain Systems with Norm Bounded Uncertainty: A Control Lyapunov Function Approach, SIAM Journal on Control and Optimization, Vol. 27, pp. 1462–1476, 1989.Google Scholar

Copyright information

© Plenum Publishing Corporation 1993

Authors and Affiliations

  • M. Corless
    • 1
  • G. Leitmann
    • 2
  1. 1.Purdue UniversityWest Lafayette
  2. 2.University of California at BerkeleyBerkeley

Personalised recommendations