THE KALMAN-YAKUBOVICH-POPOV LEMMA IN A BEHAVIORAL FRAMEWORK

The classical Kalman-Yakubovich-Popov Lemma provides a link between di ssipativity of a system in state-space form and the solution to a line ar 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 dissipat ivity problem is posed. Subsequently we study the connection between d issipativity and spectral factorization of polynomial matrices. This e nables us to derive a new algorithm for polynomial spectral factorizat ion in terms of an LMI in the coefficients of a polynomial matrix. (C) 1997 Elsevier Science B.V.