Optimalq-Markov COVER for finite wordlength implementation | Theory of Computing Systems Skip to main content
Log in

Optimalq-Markov COVER for finite wordlength implementation

  • Published:
Mathematical systems theory Aims and scope Submit manuscript

Abstract

The existingq-Markov COVER realization theory does not take into account the problems of arithmetic errors due to both the quantization of states and coefficients of the reduced-order model. Allq-Markov COVERs allow some freedom in the choice of parameters. In this paper we exploit this freedom in the existing theory to optimize the models with respect to these finite wordlength effects.

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

Access this article

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Japan)

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. B. D. O. Anderson and R. E. Skelton, The generation of allq-Markov covers,IEEE Trans. Circuits and Systems (to appear). Also seeProc. IFAC Congress, Munich, 1987.

  2. S. Y. Hwang, Minimum uncorrelated unit noise in state space digital filtering,IEEE Trans. Acoust. Speech Signal Process., Vol. 25, 1977, pp. 273–281.

    Google Scholar 

  3. M. Kawamata and T. Higuchi, A unified approach to the optimal synthesis of fixed point state space filters,IEEE Trans. Acoust. Speech Signal Process., Vol. 33, 1985, p. 911.

    Google Scholar 

  4. A. M. King, V. B. Desai, and R. E. Skelton, A generalized approach toq-Markov covariance equivalent realizations for discrete systems,Proc. 1987 ACC, Minneapolis, MN, pp. 1521–1526.

  5. P. Moroney,Issues in the Implementation of Digital Feedback Compensations, MIT Press, Cambridge, MA, 1983.

    Google Scholar 

  6. C. T. Mullis and R. A. Roberts, Synthesis of minimum roundoff noise in fixed point digital filters,IEEE Trans. Circuits and Systems, Vol. 23, 1976, pp. 256–262.

    Google Scholar 

  7. L. R. Rabiner and B. Gold,Digital Signal Processing, Prentice Hall, Englewood Cliffs, NJ, 1975.

    Google Scholar 

  8. R. E. Skelton and B. D. O. Anderson,q-Markov equivalent realizations,Internat. J. Control, Vol. 44, No. 5, 1986, pp. 1477–1490.

    Google Scholar 

  9. R. E. Skelton and E. G. Collins, Set ofq-Markov covariance equivalent models of discrete systems,Internat. J. Control, Vol. 46, No. 1, 1987, pp. 1–12.

    Google Scholar 

  10. A. B. Stripad and D. L. Snyder, A necessary and sufficient condition for quantization errors to be uniform and white,IEEE Trans. Acoust. Speech Signal Process., Vol. 25, 1977, pp. 442–448.

    Google Scholar 

  11. A. J. M. Van Wingerden and W. L. de Koning, The influence of finite wordlength on digital optimal control,IEEE Trans. Automat. Control, Vol. 29, 1984, p. 385.

    Google Scholar 

  12. D. Williamson, Finite state wordlength compensation in digital Kalman filters,IEEE Trans. Automat. Control, Vol. 30, No. 10, 1985, pp. 930–939.

    Google Scholar 

  13. D. Williamson, Structural state space sensitivity in linear systems,Systems Control Lett., Vol. 7, July 1986, pp. 301–307.

    Google Scholar 

  14. D. Williamson, Roundoff noise minimization and pole-zero sensitivity in fixed point digital filters using residue feedback,IEEE Trans. Acoust. Speech Signal Process., Vol. 34, No. 5, 1986, pp. 1210–1220.

    Google Scholar 

  15. D. Williamson, Delay replacement in direct form structures,IEEE Trans. Acoust. Speech Signal Process., Vol. 36, No. 4, 1988, pp. 453–460.

    Google Scholar 

  16. D. Williamson and K. Kadiman, The optimal fixed point linear quadratic regulator,Proc. 27th IEEE Decision & Control Conf., Dec. 1988, Austin, TX, pp. 1285–1290.

  17. D. Williamson and S. Sridharan, Residue feedback in digital filters using fractional feedback coefficients,IEEE Trans. Acoust. Speech Signal Process., Vol. 33, 1985, pp. 477–483.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Williamson, D., Skelton, R.E. Optimalq-Markov COVER for finite wordlength implementation. Math. Systems Theory 22, 255–273 (1989). https://doi.org/10.1007/BF02088302

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02088302

Keywords

Navigation