  This paper proposes a direct, and simple approach to the H infinity norm
calculation in more general settings. In contrast to the method based on the
Kalman-Yakubovich-Popov lemma, our approach does not require a controllability
assumption, and returns a sinusoidal input that achieves the H infinity norm of
the system including its frequency. In addition, using a semidefinite
programming duality, we present a new proof of the Kalman- Yakubovich-Popov
lemma, and make a connection between strong duality and controllability.
Finally, we generalize our approach towards the generalized
Kalman-Yakubovich-Popov lemma, which considers input signals within a finite
spectrum.

Optimization and Control;Systems and Control