Skip to main content
SpringerLink
Log in
Book cover

Mathematical Theory of Networks and Systems pp 406–420Cite as

Stochastic balancing and approximation-stability and minimality

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 58))

Abstract

A new method of balancing, called stochastic balancing, has recently been introduced. This paper focuses on the stability aspects of the associated stochastic model reduction scheme. It is shown that in both the continuous-time and discrete-time cases the reduced order model is asymptotically stable and dissipative. Further it is shown that in the continuous-time case the reduced order model is minimal.

This work was supported in part by ARO Grant DAAG29-79-C-0054 and JSEP Grant F44620-71-C-06067.

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. U.B. Desai & D. Pal, "A realization approach to stochastic model reductions and balanced stochastic realizations," Proc. 16th Annual Conf. on Information Sciences and Systems, Princeton University, Princeton, NJ, 1982.

    Google Scholar 

  2. Pernebo & L.M. Silverman, "Model reduction via balanced state space representation," IEEE Trans. on Automatic Control, Vol. AC-27, pp. 382–387, 1982.

    Google Scholar 

  3. P. Faurre, "Stochastic realization algorithms," in System Identification: Advances and Case Studies (Eds. R.K. Mehra & D.G. Lainiotis), Academic Press, New York, 1976.

    Google Scholar 

  4. P. Faurre & J.P. Marmorat, "Un algorithme de realisation stochastique," C.R. Acad. Sci., Paris, T.268, Serie A, April 1969, pp. 978–981.

    Google Scholar 

  5. F. Germain, "Algorithmes continus de calcul de realisations markoviennes, cas singulier et stabilite," Rapport Laboria No. 66, April 1974.

    Google Scholar 

  6. A. Lindquist & G. Picci, "On the stochastic realization problem," SIAM J. Optimal Control, Vol. 17, pp. 365–389, 1979.

    Google Scholar 

  7. B.D.O. Anderson & S. Vongpanitlerd, Network Analysis and Synthesis," Prentice-Hall, Englewood Cliffs, NJ, 1973.

    Google Scholar 

  8. T. Kailath, "A view of three decades of linear filtering theory," IEEE IT, Vol. IT-20, pp. 146–181, March 1974.

    Google Scholar 

  9. H. Kwakernaak & R. Sivan, "Linear Optimal Control Systems," Wiley-Interscience, 1972.

    Google Scholar 

  10. G.S. Sidhu & U.B. Desai, "New smoothing algorithms based on reversed-time lumped models," IEEE Trans. on Automatic Control, Vol. AC-21, pp. 538–541, 1976.

    Google Scholar 

  11. J.M. Mendel & S. Kung, "Computer Programs for Wavelet Modeling," Department of Electrical Engineering, University of Southern California, Geosignal Processing Program Report, May 1981.

    Google Scholar 

  12. E.A. Jonckheere & L.M. Silverman, "A new set of invariants for linear systems — application to reduced order compensator design," to appear in the June 1983 issue of IEEE Trans. on Automatic Control.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical Engineering-Systems, University of Southern California, 90089-0781, Los Angeles, CA, USA

    P. Harshavardhana, E. A. Jonckheere & L. M. Silverman

Authors
  1. P. Harshavardhana
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. A. Jonckheere
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. L. M. Silverman
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

P. A. Fuhrmann

Rights and permissions

Reprints and permissions

Copyright information

© 1984 Springer-Verlag

About this paper

Cite this paper

Harshavardhana, P., Jonckheere, E.A., Silverman, L.M. (1984). Stochastic balancing and approximation-stability and minimality. In: Fuhrmann, P.A. (eds) Mathematical Theory of Networks and Systems. Lecture Notes in Control and Information Sciences, vol 58. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0031070

Download citation

  • DOI: https://doi.org/10.1007/BFb0031070

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13168-7

  • Online ISBN: 978-3-540-38826-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation