Skip to main content

A New Tool for Robust Control

  • Chapter
Mechanics and Control

Abstract

We present a new tool for the analysis and design of uncertain linear systems. A robustness measure is developed based on the characteristic equation root locations. This measure has a useful geometric interpretation.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. K. J. Astrom, Introduction to Stochastic Control Theory Academic Press, New York, 1970.

    Google Scholar 

  2. B. R. Barmish and P.P. Khargonekar, “Robust stability of feedback control systems with uncertain parameters and unmodeled dynamics,” Proceedings of American Control Conference Atlanta, Georgia, 1988.

    Google Scholar 

  3. B. R. Barmish and R. Tempo, “The robust root locus,” Automatica, Vol. 26, pp. 283–292, 1990.

    Article  MathSciNet  MATH  Google Scholar 

  4. C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers McGraw-Hill, New York, 1989.

    Google Scholar 

  5. N. K. Bose and E. Zeheb, “Kharitonov’s theorem and stability test of multidimensional digital filters,” IEE Proceedings-G Vol. 133, pp. 187–190, 1986.

    MathSciNet  Google Scholar 

  6. N. K. Bose, “Robust multivariate scattering Hurwitz interval polynomials,” Linear Algebra and its Applications, Vol. 98, pp. 123–136, 1988.

    Article  MATH  Google Scholar 

  7. C. T. Chen, Introduction to Linear Systems Theory Holt, Rinehart and Winston, New York, 1970.

    Google Scholar 

  8. R. C. Dorf, Modern Control Systems Addison-Wesley, Reading, Mass., 1992.

    Google Scholar 

  9. L. R. Fletcher, J. Kautsky, G. K. G. Kolka and N. K. Nichols, “Some necessary and sufficient conditions for eigenstructure assignment,” Int. J. Cont. Vol. 42, pp. 1457–68, 1985.

    Article  MathSciNet  MATH  Google Scholar 

  10. G. F. Franklin, J. D. Powell and A. Emami-Naeini, Feedback Control of Dynamic Systems Addison-Wesley, Reading, Mass., 1991.

    Google Scholar 

  11. J. Kautsky, N. K. Nichols and P. van Dooren, “Robust pole assignment in linear state feedback,” Int. J. Cont. Vol. 41, pp. 1129–55, 1985.

    Article  MATH  Google Scholar 

  12. B. C. Kuo, Automatic Control Systems Prentice-Hall, Englewood Cliffs, New Jersey, 1975.

    Google Scholar 

  13. G. Leitmann, “Deterministic control of uncertain systems,” Acta Astronautica Vol. 7, pp. 1457–61, 1980.

    Article  MATH  Google Scholar 

  14. N. A. Letomaki, N. R. Snadell and M. Athans, “Robustness results in linear quadratic Gaussian based multivariable control design,” IEEE Trans. Autom. Cont. Vol. 26, pp. 75–93, 1981.

    Article  Google Scholar 

  15. T. Mori and H. Kokame, “An extension of Kharitonov’s theorem and its application,” Proceedings of American Control Conference Minneapolis, Minnesota, 1987.

    Google Scholar 

  16. J. H. Wilkinson, “The evaluation of zeros of ill-conditioned polynomials,” Num. Math. Vol. 1, pp. 150–180, 1959.

    MathSciNet  Google Scholar 

  17. J. H. Wilkinson, Rounding Errors in Algebraic Processes Prentice-Hall, Englewood Cliffs, New Jersey, 1963.

    Google Scholar 

  18. G. Zames, “Feedback and optimal sensitivity: Model reference transformations, multiplicative seminorms, and approximate inverses,” IEEE Trans. Autom. Cont. Vol. 26, pp. 301–20, 1981.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer Science+Business Media New York

About this chapter

Cite this chapter

Soldatos, A.G., Chung, C., Auslander, D.M. (1994). A New Tool for Robust Control. In: Guttalu, R.S. (eds) Mechanics and Control. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2425-0_7

Download citation

  • DOI: https://doi.org/10.1007/978-1-4615-2425-0_7

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-6029-2

  • Online ISBN: 978-1-4615-2425-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics