The Kalman-Yakubovich-Popov lemma in a behavioural framework

R.A.B. van der Geest, Robert van der Geest, Harry Trentelman

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    Abstract

    The classical Kalman-Yakubovich-Popov Lemma provides a link between dissipativity of a system in state-space form and the solution to a linear matrix inequality. In this paper we derive the KYP Lemma for linear systems described by higher-order differential equations. The result is an LMI in terms of the original coefficients in which the dissipativity problem is posed. Subsequently we study the connection between dissipativity and spectral factorization of polynomial matrices. This enables us to derive a new algorithm for polynomial spectral factorization in terms of an LMI in the coefficients of a polynomial matrix.
    Original languageUndefined
    Pages (from-to)283-290
    Number of pages8
    JournalSystems and control letters
    Volume32
    Issue number5
    DOIs
    Publication statusPublished - 1997

    Keywords

    • Polynomial spectral factorization
    • Dissipative systems theory
    • Linear matrix inequalities
    • Two-variable polynomial matrices
    • METIS-140299
    • IR-29665

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