This paper is concerned with the problem of synthesizing finite frequency H-infinity dynamic controllers which contain an internal model of desired modes for continuous-time linear systems. A state-space design method is proposed using the generalized Kalman-Yakubovich-Popov (GKYP) lemma with the feature that the degree of freedom of the numerator of the internal model can be fully exploited for the design. Numerical examples are provided for applications such as narrow-band disturbance attenuation and proportional-integral-derivative (PID) controller design that demonstrates the effectiveness of the proposed method.
