Generalization of Kalman-Yakubovic-Popov lemma for restricted frequency inequalities

The celebrated Kalman-Yakubovic-Popov (KYP) lemma converts frequency domain inequalities to linear matrix inequalities in the state space, suitable for development of systems theory and for numerical computations. This paper generalizes the KYP lemma to treat conditions on restricted frequency intervals. Conditions for both continuous-time and discrete-time cases are obtained as special cases.