Dynamics and Control

, Volume 6, Issue 2, pp 131–142 | Cite as

Performance analysis of controlled uncertain systems

  • Y. H. Chen
Article

Abstract

Robust control which is designed via the Lyapunov approach has been shown to be effective for nonlinear uncertain systems. The performance of the controlled systems is studied by the Lyapunov argument. We propose to use the comparison principle which is based on the differential inequality to further explore the performance of controlled uncertain systems.

Keywords

Control System Performance Analysis Robust Control Comparison Principle Uncertain System 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ambrosino, G., Celentano, G., and Garofalo, F., “Robust model tracking for a class of nonlinear plants,”IEEE Transactions on Automatic Control, vol. 30, pp. 275–279, 1985.Google Scholar
  2. 2.
    Barmish, B. R., Corless, M., and Leitmann, “A new class of stabilizing controllers for uncertain dynamical systems,”SIAM Journal of Control and Optimization, vol. 21, pp. 246–255, 1983.Google Scholar
  3. 3.
    Birkhoff, G., and Rota, G-C., Ordinary Differential Equations, Blaisdell: Waltham, Massachusetts, 1962.Google Scholar
  4. 4.
    Chen, Y. H., “On the deterministic performance of uncertain dynamical systems,”International Journal of Control, vol. 43, no. 5, pp. 1557–1579, 1986.Google Scholar
  5. 5.
    Chen, Y. H., and Leitmann, G., “Robustness of uncertain systems in the absence of matching assumptions,”International Journal of Control, vol. 45, pp. 1527–1542, 1987.Google Scholar
  6. 6.
    Corless, M., “Guaranteed rates of exponential convergence for uncertain systems,”Journal of Optimization Theory and Applications, vol. 76, pp. 471–484, 1990.Google Scholar
  7. 7.
    Corless, M., “Control of uncertain nonlinear systems,”Journal of Dynamic Systems, Measurement, and Control, vol. 115, pp. 362–372, 1993.Google Scholar
  8. 8.
    Corless, M. J., and Leitmann, G., “Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems,”IEEE Transactions on Automatic Control, vol. 26, pp. 1139–1144, 1981.Google Scholar
  9. 9.
    Corless, M., and Leitmann, G., “Adaptive control of systems containing uncertain functions and unknown functions with uncertain bounds,”Journal of Optimization Theory and Applications, vol. 41, pp. 155–168, 1983.Google Scholar
  10. 10.
    Garofalo, F., and Leitmann, G., “Guaranteeing ultimate boundedness and exponential rate of convergence for a class of nominally linear uncertain systems,”Journal of Dynamic Systems, Measurement, and Control, vol. 111, pp. 584–589, 1989.Google Scholar
  11. 11.
    Han, M. C., and Chen, Y. H., “Polynomial robust control design for uncertain systems,”Automatica, vol. 28, pp. 809–814, 1992.Google Scholar
  12. 12.
    Gutman, S., “Uncertain dynamical systems: a Lyapunov min-max approach,”IEEE Transactions on Automatic Control, vol. 24, pp. 437–443, 1979; correction, vol. 25, p. 613, 1980.Google Scholar
  13. 13.
    Hale, J. K.,Ordinary Differential Equations, Krieger: Huntington, 1969.Google Scholar
  14. 14.
    Leitmann, G., “On the efficacy of nonlinear control in uncertain linear systems,”Journal of Dynamic Systems, Measurement, and Control, vol. 103, pp. 95–102, 1981.Google Scholar
  15. 15.
    Leitmann, G., “On one approach to the control of uncertain systems,”Journal of Dynamic Systems, Measurement, and Control, vol. 115, pp. 373–380, 1993.Google Scholar
  16. 16.
    Leitmann, G., “One approach to the control of uncertain dynamical systems,”Sixth Workshop of Dynamics and Control, Vienna, Austria, 1993.Google Scholar
  17. 17.
    Murphy, G.M.,Ordinary Differential Equations and Their Solutions, D. Van Nostrand Company, Inc.: Princeton, New Jersey, 1960.Google Scholar
  18. 18.
    Pandey, S., Leitmann, G., and Corless, M., “A deterministic controller for a new class of uncertain systems,”Proceedings of the IEEE Conference on Decision and Control, pp. 2615–2617, 1991.Google Scholar
  19. 19.
    Petersen, I. R., and Hollot, C. V., “A Riccati equation approach to the stabilization of uncertain linear systems,”Automatica, vol. 22, no. 4, pp. 397–411, 1986.Google Scholar
  20. 20.
    Siljak, D. D., 1978,Large-Scale Dynamical Systems: Stability and Structure, North-Holland: New York, 1978.Google Scholar
  21. 21.
    Zwillinger, D.,Handbook of Differential Equations, Second Edition, Academic Press: San Diego, 1992.Google Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Y. H. Chen
    • 1
  1. 1.The George W. Woodruff School of Mechanical EngineeringGeorgia Institute of TechnologyAtlantaUSA

Personalised recommendations