New algorithms for polynomial J-spectral factorization

HL Trentelman*, P Rapisarda

*Corresponding author for this work

    Research output: Contribution to journalArticleAcademicpeer-review

    39 Citations (Web of Science)


    In this paper new algorithms are developed for J-spectral factorization of polynomial matrices. These algorithms are based on the calculus of two-variable polynomial matrices and associated quadratic differential forms, and share the common feature that the problem is lifted from the original one-variable polynomial context to a two-variable polynomial context. The problem of polynomial J-spectral factorization is thus reduced to a problem of factoring a constant matrix obtained from the coefficient matrices of the polynomial matrix to be factored. In the second part of the paper, we specifically address the problem of computing polynomial J-spectral factors in the context of H-infinity control. For this, we propose an algorithm that uses the notion of a Pick matrix associated with a given two-variable polynomial matrix.

    Original languageEnglish
    Pages (from-to)24-61
    Number of pages38
    JournalMathematics of Control Signals and Systems
    Issue number1
    Publication statusPublished - 1999


    • polynomial J-spectral factorization
    • two-variable polynomial matrix
    • quadratic differential form
    • dissipativity
    • Pick matrix

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