The L<inf>∞</inf>=L<inf>2</inf> Hankel 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 -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.