Hostname: page-component-848d4c4894-tn8tq Total loading time: 0 Render date: 2024-06-20T23:53:47.817Z Has data issue: false hasContentIssue false
  • English
  • Français

On the continuity of the Wiener-Hopf factorization operation

Published online by Cambridge University Press:  17 February 2009

Michael Green  and
Brian D.O. Anderson
Michael Green
Affiliation:
Department of Systems Engineering, Research School of Physical Sciences, Australian National University, G.P.O. Box 4, Canberra, A.C.T., 2601, Australia.
Brian D.O. Anderson
Affiliation:
Department of Systems Engineering, Research School of Physical Sciences, Australian National University, G.P.O. Box 4, Canberra, A.C.T., 2601, Australia.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The problem of passing from an L∞ function to a Wiener-Hopf factorization is considered. It is shown that a small L∞ perturbation which does not change the factorization indices will lead to small Lp (1 < p < ∞) perturbations in the Wiener-Hopf factors, but can lead to large L∞ perturbations, unless the derivatives are controlled during the perturbation.

Type
Research Article
Information
The ANZIAM Journal , Volume 28 , Issue 4 , April 1987 , pp. 443 - 461
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Anderson, B. D. O., “Continuity of the matrix spectral factorization operation”, Mat. Appl. Comput. (to appear).Google Scholar
[2]Anderson, B. D. O. and Gevers, M., “Identifiability of linear stochastic systems operating under linear feedback”, Automatica 18 (1982), 195–213.CrossRefGoogle Scholar
[3]Anderson, B. D. O. and Moore, J. B., Linear Optimal Control (Prentice Hall, Englewood Cliffs, N. J., 1971).Google Scholar
[4]Clancey, K. and Gohberg, I., Factorization of Matrix Functions and Singular Integral Operators (Birkhauser, Verlag, Basel, 1981).Google Scholar
[5]Desoer, C. and Vidyasagar, M., Feedback Systems: Input-Output Properties (Academic Press, New York, 1975).Google Scholar
[6]Francis, B. A., “On robustness of the stability of feedback systems”, IEEE Trans. Automat. Control, 25 (1980), 817–818.CrossRefGoogle Scholar
[7]Gohberg, I. and Fel'dman, I., “Convolution Equations and Projection Methods for their Solution”, Amer.Math. Soc. Transl. 1974.Google Scholar
[8]Gohberg, I. and Goldberg, S., Basic Operator Theory (Birkhauser, Verlag, Basel, 1981).CrossRefGoogle Scholar
[9]Gohberg, I. and Krein, M., “Systems of integra1 equations on a half line with kernels depending on the difference of arguments”, Uspekhi Mat. Nauk, 13, No. 2 (80) (1958), 3–72;Google Scholar
Amer. Math. Soc. Transl. 2 (1960),217–287.Google Scholar
[10]Green, M. and Anderson, B. D. O., “Identification of multivariable errors-in-variables models with dynamics”, IEEE Trans. Automat. Control. 31 (1986), 467–471.Google Scholar
[11]Royden, H., Real Analysis (Macmillan, New York, 1963).Google Scholar
[12]Rozanov, Y.A., Stationary Random Processes (Holden-Day, San Francisco, 1963).Google Scholar
[13]Wiener, N., The Fourier Integral and Certain of its Applicaitons (Cambridge University Press, London, 1933).Google Scholar
[14]Wiener, N. and Masani, P., “The prediction theory of multivariate stochastic processes, parts 1 and 2” Acta Math. 98 (1957), 111–150; 99, (1958), 93–137.CrossRefGoogle Scholar
[15]Youla, D.C., “On the factorizaiton of rational matrices”, IEEE Trans. Inform. Theory, 17 (1961), 172–189.CrossRefGoogle Scholar