The Kalman-Yakubovich-Popov Lemma in a behavioural framework

R van der Geest*, H Trentelman

*Corresponding author for this work

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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. (C) 1997 Elsevier Science B.V.

Original languageEnglish
Pages (from-to)283-290
Number of pages8
JournalSystems & Control Letters
Issue number5
Publication statusPublished - 19-Dec-1997


  • dissipative systems theory
  • two-variable polynomial matrices
  • linear matrix inequalities
  • polynomial spectral factorization

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