Generalized KYP Lemma With Real Data

A recent generalization of the Kalman-Yakubovich-Popov (KYP) lemma establishes the equivalence between a semi-infinite inequality on a segment of a line or circle in the complex plane and a linear matrix inequality (LMI). In this technical note we show that when the data are real, the matrix variables in the LMI can be restricted to be real, even when the frequency range is asymmetric with respect to the real axis.