H infinity Analysis Revisited

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.