On Kalman-Yakubovich-Popov lemma for stabilizable systems

The Kalman-Yakubovich-Popov (KYP) lemma has been a cornerstone in system theory and network analysis and synthesis. It relates an analytic property of a square transfer matrix in the frequency domain to a set of algebraic equations involving parameters of a minimal realization in the time domain. This note proves that the KYP lemma is also valid for realizations which are stabilizable and observable.

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