Generalizing the KYP lemma to the union of intervals

A recent generalization of the Kalman-Yakubovich-Popov (KYP) lemma establishes the equivalence between a semi-infinite inequality on a segment of a circle or straight line in the complex plane and a linear matrix inequality. In this paper we further generalize the KYP lemma to particular curves in the complex plane, which include the union of segments of a circle or line as a special case.