Properties of the Quasi L_2/L_2 Hankel Norms and the L_2/L_2 Hankel Operator of Sampled-Data Systems

摘要

This paper aims at appropriately defining the L_2/L_2 Hankel operator and L_2/L_2 Hankel norm of sampled-data systems through setting a general time instant Θ at which the past and future is separated and introducing the associated quasi L_2/L_2 Hankel operator/norm at Θ. We first provide a method for computing the quasi L_2/L_2 Hankel norm for each Θ. We then discuss some important properties of the quasi L_2/L_2 Hankel norms over a sampling interval and show that the supremum of these norm is attained, and thus the L_2/L_2 Hankel operator always exists for stable sampled-data systems.