Characterization of Quasi L-infinity/L-2 Hankel Norms of Sampled-Data Systems

Abstract

This paper is concerned with the Hankel operator of sampled-data systems. The Hankel operator is usually defined as a mapping from the past input to the future output and its norm plays an important role in evaluating the performance of systems. Since the continuous time mapping between the input and output is periodically time-varying (h-periodic, where h denotes the sampling period) in sampled-data systems, it matters when to take the time instant separating the past and the future when we define the Hankel operator for sampled-data systems. This paper takes an arbitrary theta is an element of [0, h) as such an instant, and considers the quasi L-infinity/L-2 Hankel operator defined as the mapping from the past input in L-2 ( -infinity, 0) to the future output in L-infinity[Theta, infinity). The norm of this operator, which we call the quasi L-infinity/L-2 Hankel norm at Theta, is then characterized in such a way that its numerical computation becomes possible. Then, regarding the computation of the L-infinity/L-2 Hankel norm defined as the supremum of the quasi L-infinity /L-2 Hankel norms over theta is an element of [0, h), some relationship is discussed between the arguments through such characterization and an alternative method developed in an earlier paper that is free from the computations of quasi L-infinity/L-2 Hankel norms. A numerical example is studied to confirm the validity of the arguments in this paper. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.