Skip to main content

Necessary conditions for optimal disturbance rejection in linear systems

  • Chapter
  • First Online:
Optimal Control with a Worst-Case Performance Criterion and Applications

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 145))

  • 176 Accesses

Abstract

Disturbance rejection is an important factor in the synthesis of controllers for several practical systems. In this chapter we derive necessary conditions which need to be satisfied by the controller which yields maximum disturbance rejection. Necessary conditions for maximum disturbance rejection are also derived in the case of an observer-based controller. These conditions are useful in the synthesis of a controller which maximizes the disturbance rejection capacity of the system. The problem considered has connections to the H control theory. An example is given.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. Doyle, K. Glover, P. Khargonekar and B. Francis, State-space solutions to standard H2 and H control problems, IEEE Trans. Automat. Contr.34, 1989, pp. 831–847.

    Google Scholar 

  2. K. Glover and J. C. Doyle, State space formulae for all stabilizing controllers that satisfy an H-norm bound and relations to risk sensitivity, Systems and Control Letters11, 1988, pp. 167–172.

    Google Scholar 

  3. H. Kimura and R. Kawatani, “Synthesis of H controllers based on conjugation,” Proc. 27th IEEE Conference on Decision and Control, 1988, pp. 7–13.

    Google Scholar 

  4. D. S. Bernstein and W. M. Haddad, LQG control with an H performance bound: A Riccati equation approach, IEEE Trans. Automat. Contr.34, 1989, pp. 293–305.

    Google Scholar 

  5. P. P. Khargonekar, I. R. Petersen and M. A. Rotea, H-optimal control with state-feedback, IEEE Trans. Automat. Contr.33, 1988, pp. 786–788.

    Google Scholar 

  6. P. P. Khargonekar, I. R. Petersen and K. Zhou, Robust stabilization and H-optimal control, 1987.

    Google Scholar 

  7. G. Tadmor, H in the time domain: The standard four block problem, Mathematics of Control, Signals, and Systems, to be published.

    Google Scholar 

  8. M. B. Subrahmanyam, On integral inequalities associated with a linear operator equation, Proc. Amer. Math. Soc.92, 1984, pp. 342–346.

    Google Scholar 

  9. M. B. Subrahmanyam, On applications of control theory to integral inequalities: II, SIAM J. Contr. Optimiz. 19, 1981, pp. 479–489.

    Google Scholar 

  10. M. B. Subrahmanyam, Necessary conditions for minimum in problems with nonstandard cost functionals, J. Math. Anal. Appl. 60, 1977, pp. 601–616.

    Google Scholar 

  11. E. B. Lee and L. Markus, “Foundations of Optimal Control Theory,” Wiley, New York, 1967.

    Google Scholar 

  12. A. S. Bratus and A. P. Seiranyan, Sufficient conditions for an extremum in eigenvalue optimization problems, PMM U.S.S.R. (Journal of Applied Mathematics and Mechanics, English translation)48, 1984, pp. 466–474.

    Google Scholar 

  13. I. Tadjbakhsh and J. B. Keller, Strongest columns and isoperimetric inequalities for eigenvalues, ASME J. Appl. Mech.29, 1962, pp. 159–164.

    Google Scholar 

Download references

Editor information

M. Bala Subrahmanyam

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag

About this chapter

Cite this chapter

(1990). Necessary conditions for optimal disturbance rejection in linear systems. In: Subrahmanyam, M.B. (eds) Optimal Control with a Worst-Case Performance Criterion and Applications. Lecture Notes in Control and Information Sciences, vol 145. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0043625

Download citation

  • DOI: https://doi.org/10.1007/BFb0043625

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52822-7

  • Online ISBN: 978-3-540-47158-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics