The L∞=L2 Hankel norm of sampled-data systems

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
-type norm for the past input and the L
∞
-type 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
-type norm were also considered on the future output.