On symmetric extraction polynomial matrix spectal factorization

  • F. M. Callier
Session 6 Linear Systems I
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 62)


We report a revision, [1], of the 1963 Davis algorithm for the spectral factorization of a parahermitian nonnegative polynomial matrix φ by symmetric factor extraction: this algorithm is careless about zeros at infinity. By introducing the notion of diagonal reducedness of φ we obtain an easy sufficient test for the absence of zeros at infinity. We show then i) how to get φ diagonally reduced by diagonal excess reduction steps, removing all zeros at infinity and ii) how to remove symmetrically finite zeros while keeping φ diagonally reduced, (whence free of zeros at infinity). Didactical examples are given. This results in a revised symmetric extraction spectral factorization algorithm with monotone degree control.


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  1. [1]
    F.M. Callier, "On Polynomial Matrix Spectral Factorization by Symmetric Extraction", Report 83/10, Department of Mathematics, Facultés Universitaires de Namur, Namur, Belgium; submitted to the IEEE Transactions on Auto. Control.Google Scholar
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    M.C. Davis, "Factoring the Spectral Matrix", IEEE Trans. Auto. Control, Vol. AC-8, pp. 296–305, 1963.Google Scholar
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    F.M. Callier and C.A. Desoer, "Multivariable Feedback Systems", Springer Verlag, New York, 1982.Google Scholar
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    V. Kučera, "New Results in State Estimation and Regulation", Automatica, Vol. 17, pp. 745–748, 1981.Google Scholar
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    F.M. Callier, "Partially Stable LQ-Optimal Control by Spectral Factorization", Int. Jour. Control, to appear, 1984.Google Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • F. M. Callier
    • 1
  1. 1.Senior Member IEEE Department of MathematicsFacultés Universitaires N.-D. de la PaixNamurBelgium

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