Upper and lower bounds of the frequency response gain of sampled-data systems

This paper gives three independent methods to compute the upper and lower b ounds of the norm of the frequency response operator of sampled-data system s. They are useful first in its own right (as an approximate method), and m ore importantly as a method to provide an effective set of the initial uppe r and lower bounds for the recently-developed bisection algorithm. It is al so shown that our arguments have very close relationships to the sampled-da ta H-2 and H-x problems. (C) 2001 Elsevier Science Ltd. All rights reserved .