Skip to main content
SpringerLink
Log in
Book cover

Modelling and Application of Stochastic Processes pp 193–214Cite as

Realization and Reduction of S.I.S.O. Nonminimum Phase Stochastic Systems

  • Chapter

Abstract

We consider the order reduction problem for single-input/ single-output (SISO) nonminimum phase linear stochastic systems. First, the realization of SISO state-space models for stationary processes generated by time-invariant finite-order, possibly nonminimum phase, linear systems is considered. It is shown that in order to obtain a “correct” phase realization, it is necessary to consider some higher-order statistics of the process in addition to the usual second-order statistics. A model in the controllable canonical form is obtained by utilizing a partial set of second- and fourth- order cumulant functions of the process. Next, model approximation by order reduction is defined in this framework. An example is presented to illustrate the proposed method.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Baram, Y. and Be’eri, Y., IEEE Trans. Automatic Control, vol. AC-26, pp. 379–390, April 1981.

    Article  Google Scholar 

  2. Baram, Y., IEEE Trans. Automatic Control, vol. AC-26, pp. 1225–1231, Dec. 1981.

    Article  MathSciNet  Google Scholar 

  3. Desai, U.B. and Pal, D., in Proc. 21st IEEE Conf. Decision and Control, pp. 1105–1112, Orlando, FL, Dec. 1982.

    Google Scholar 

  4. Larimore, W.E., in Proc. 1983 American Control Conf., pp. 445–451, San Francisco, CA, June 1983.

    Google Scholar 

  5. Arun, K.S., Bhaskar Rao, D.V., and Rung, S.Y., in Proc. 22nd IEEE Conf. Decision and Control, pp. 1353–1355, San Antonio, TX, Dec. 1983.

    Chapter  Google Scholar 

  6. Vaccaro, R.J., in Proc. 1984 American Control Conference, pp. 393–396, San Diego, CA, June 1984.

    Google Scholar 

  7. Wagie, D.A. and Skelton, R.E., in Proc. 23rd IEEE Conf. Decision and Control, pp. 133–138, Las Vegas, NV, Dec. 1984.

    Chapter  Google Scholar 

  8. Genesio, R. and Milanese, R., IEEE Trans. Automatic Control, vol. AC-21, pp. 118–122, Feb. 1976.

    Article  MathSciNet  Google Scholar 

  9. Hickin, J. and Sinha, N.K., IEEE Trans. Automatic Control, vol. AC-25, pp.1121–1127, Dec. 1980.

    Article  Google Scholar 

  10. Moore, B.C., IEEE Trans. Automatic Control, vol. AC-26, pp. 17–32, Feb. 1981.

    Article  Google Scholar 

  11. Mendel, J.M., Optimal Seismic Deconvolution. New York: Academic Press, 1983.

    Google Scholar 

  12. Freudenberg, J.S. and Looze, D.P., in Proc. 22nd IEEE Conf. Decision and Control, San Antonio, TX, pp. 625–630, Dec. 1983.

    Chapter  Google Scholar 

  13. Benveniste, A., Goursat, M. and Rüget, G., IEEE Trans. Automatic Control, vol. AC-25, pp. 385–398, June 1980.

    Article  Google Scholar 

  14. Anderson, B.D.O. and Moore, J.B., Optimal Filtering. Englewood Cliffs, N.J.: Prentice-Hall, 1979.

    MATH  Google Scholar 

  15. Lii, K.S. and Rosenblatt, M., Annals of Statistics, vol. 10, pp. 1195–1208, 1982.

    Article  MathSciNet  MATH  Google Scholar 

  16. Brillinger, D.R., Annals Math. Statistics, vol. 36, pp. 1351–1374, 1965.

    Article  MathSciNet  MATH  Google Scholar 

  17. Brillinger, D.R. and Rosenblatt, M., in Spectral Analysis of Time Series, B.Harris (ed.), New York: Wiley, 1967, pp. 153–188.

    Google Scholar 

  18. Brillinger, D.R. and Rosenblatt, M., in Spectral Analysis of Time Series, B.Harris (ed.), New York: Wiley, 1967, pp. 189–232.

    Google Scholar 

  19. Tugnait, J.K., in Proc. 23rd IEEE Conf. Decision and Control, pp. 342–347, Las Vegas, NV, Dec. 1984. (Also, to appear in Automatica, 1986.)

    Chapter  Google Scholar 

  20. Mehra, R.K., IEEE Trans. Automatic Control, vol. AC-16, pp. 12–21, Feb. 1971.

    Article  MathSciNet  Google Scholar 

  21. Bitmead, R.R., IEEE Trans. Automatic Control, vol. AC-26, pp. 11–1294, Dec. 1981.

    MathSciNet  Google Scholar 

  22. Astrom, K.J., Automatica, vol. 16, pp. 551–574, 1980.

    Article  Google Scholar 

  23. Gantmacher, F.R., Applications of the Theory of Matrices. New York: Inter- science, 1959.

    MATH  Google Scholar 

  24. Dennis, J.E., Jr. and Schnabel, R.B., Numerical Methods for Unconstrained Optimisation and Nonlinear Equations. Englewood Cliff, NJ: Prentice-Hall, 1983, (Sec. 10.3).

    Google Scholar 

  25. [25]Tugnait, J.K., IEEE Trans. Automatic Control, to appear.

    Google Scholar 

  26. Kendall, M.G. and Stuart, A., The Advanced Theory of Statistics, Vol. I. New York: Macmillan, 4th Edition, 1977.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Exxon Production Research Company, P.O. Box 2189, Houston, TX, 77252-2189, USA

    Jitendra K. Tugnait

Authors
  1. Jitendra K. Tugnait
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Washington State University, Pullman, Washington, USA

    Uday B. Desai

Rights and permissions

Reprints and permissions

Copyright information

© 1986 Kluwer Academic Publishers, Boston

About this chapter

Cite this chapter

Tugnait, J.K. (1986). Realization and Reduction of S.I.S.O. Nonminimum Phase Stochastic Systems. In: Desai, U.B. (eds) Modelling and Application of Stochastic Processes. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-2267-2_8

Download citation

  • DOI: https://doi.org/10.1007/978-1-4613-2267-2_8

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4612-9400-9

  • Online ISBN: 978-1-4613-2267-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation