H infinity Analysis Revisited

—This paper proposes a direct, and simple approach to the H∞ 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∞ 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.