Skip to main content
SpringerLink
Log in

Spectral methods for the solution of linear descriptor systems using Fourier functions

  • Published:
Circuits, Systems and Signal Processing Aims and scope Submit manuscript

Abstract

In this paper a spectral method using orthogonal periodic basis functions for the analysis of linear time invariant descriptor systems is discussed, and the case of the trigonometric Fourier functions is investigated in detail. The method is shown to be convergent, in the distributional sense. However, for any finite number of basis functions, the periodicity induced by the chosen basis can give rise to spurious impulsive components in the computed system response, even in the case of correct initial conditions.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. CF. Chen and C.H. Hsiao, Design of piecewise constant gains for optimal control via Walsh functions,IEEE Trans. Auto. Cont., vol. AC-20, pp. 596–603, October, 1975.

    Google Scholar 

  2. T.T. Lee and Y.F. Tsay, Applications of general discrete orthogonal polynomials to optimal control systems,Int. J. Cont., vol. 43, pp. 1375–1386, 1986.

    Google Scholar 

  3. N.K. Bose and S. Basu, Two-dimensional matrix Pade approximants: existence, non-uniqueness and recursive computation,IEEE Trans. Auto. Cont., vol. AC-25, pp. 509–514, June, 1980.

    Google Scholar 

  4. P.N. Parakevopoulos, Chebychev series approach to system identification, analysis and optimal control,J. Franklin Inst., vol. 316, pp. 135–157, 1983.

    Google Scholar 

  5. P.N. Paraskevopoulos, Analysis of singular systems using orthogonal functions,IEE Proc. D., vol. 131, pp. 37–38, January, 1984.

    Google Scholar 

  6. F.L. Lewis and G.B. Mertzios, Analysis of singular systems using orthogonal functions,IEEE Trans. Auto. Cont., vol. AC-32, pp. 527–530, June, 1987.

    Google Scholar 

  7. A. Caiti and G. Cannata, Regularization techniques for the analysis of singular dynamic systems,Proc. 29th IEEE Conf. Deci. and Cont., Honolulu, HI, pp. 3603–3606, December, 1990.

  8. A. Caiti and G. Cannata, On the stability of spectral methods for the numerical solution of descriptor systems,Proc. 13th IMACS World Cong. Comp. and Appl. Math., Dublin, Ireland, pp. 453–454, July, 1991.

  9. W. Marszalek, Orthogonal function analysis of singular systems with impulsive response,IEE Proc. D, vol. 137, pp. 84–86, March, 1990.

    Google Scholar 

  10. S.L. Campbell and K.D. Yeomans, Solving singular systems using orthogonal functions,IEE Proc. D, vol. 137, pp. 222–224, July, 1990.

    Google Scholar 

  11. P.N. Paraskevopoulos, The operational matrices of integration and differentiation for the Fourier sine-cosine and exponential series,IEEE Trans. Auto. Cont., vol. AC-32, pp. 648–651, July, 1987.

    Google Scholar 

  12. L. Dai,Singular Control Systems, Springer-Verlag, Berlin, 1989.

    Google Scholar 

  13. R. Beals,Advanced Mathematical Analysis, Springer-Verlag, New York, 1973.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Saclant Undersea Research Centre, DIST University of Genova, Via San Bartolomeo 400, 19138, La Spezia, Italy

    Andrea Caiti

  2. Italian National Research Council, IAN-CNR Naval Automation Institute, Viale Causa 18r, 16145, Genova, Italy

    Giorgio Cannata

Authors
  1. Andrea Caiti
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Giorgio Cannata
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work has been partially funded by MURST 4010 project “Identificazione di modelli, controllo di sistemi, elaborazione di segnali.”

Rights and permissions

Reprints and permissions

About this article

Cite this article

Caiti, A., Cannata, G. Spectral methods for the solution of linear descriptor systems using Fourier functions. Circuits Systems and Signal Process 13, 225–239 (1994). https://doi.org/10.1007/BF01188108

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01188108

Keywords

Search

Navigation