H infinity Analysis Revisited

• DOI: 10.48550/arxiv.1412.6160
• Publication Date: 2014-01-01
• Authors: You, Seungil; Gattami, Ather
• Keywords: 0203 mechanical engineering; Optimization and Control (math.OC); FOS: Mathematics; FOS: Electrical engineering, electronic engineering, information engineering; 02 engineering and technology; Systems and Control (eess.SY); Mathematics - Optimization and Control; Electrical Engineering and Systems Science - Systems and Control

Submitted to IEEE Transactions on Automatic Control<br/>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.<br/>