The L∞/L2 Hankel operator/norm of sampled-data systems

Abstract

This paper is concerned with the Hankel operator and the Hankel norm of sampled-data systems. Even though these systems are intrinsically periodically time-varying, no studies have taken this important feature into account in the treatment of the Hankel operator/norm. We characterize the Hankel operator/norm of sampled-data systems adequately under the treatment with the L-2 norm for the past input and the L-infinity norm for the future output. Such treatment still captures the essential issue on the periodicity but contributes to neat arguments compared with the case when the L-2 norm is also considered on the future output.