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    Solvability conditions for the positive real lemma equations in the discrete time

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    Authors
    Ferrante, A.
    Ntogramatzidis, Lorenzo
    Date
    2017
    Type
    Journal Article
    
    Metadata
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    Citation
    Ferrante, A. and Ntogramatzidis, L. 2017. Solvability conditions for the positive real lemma equations in the discrete time. IET Control Theory and Applications. 11 (16): pp. 2916-2920.
    Source Title
    IET Control Theory and Applications
    DOI
    10.1049/iet-cta.2017.0314
    ISSN
    1751-8644
    School
    Department of Mathematics and Statistics
    URI
    http://hdl.handle.net/20.500.11937/57714
    Collection
    • Curtin Research Publications
    Abstract

    Passivity theory and the positive real lemma have been recognised as two of the cornerstones of modern systems and control theory. As digital control is pervasive in virtually all control applications, developing a general theory on the discretetime positive real lemma appears to be an important issue. While for minimal realisations the relations between passivity, positive-realness and existence of solutions of the positive real lemma equations is very well understood, it seems fair to say that this is not the case in the discrete-time case, especially when the realisation is non-minimal and no conditions are assumed on left-and/or right-invertibility of the transfer function. The purpose of this study is to present a necessary and sufficient condition for existence of solutions of the positive real equations under the only assumption that the state matrix A is asymptotically stable.

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