Is set modeling of white noise a good tool for robust H analysis?

Recently, a new deterministic characterization of the H 2 norm has been proposed, using a new norm (DD . DD Wg ), based on (approximate) set membership modeling of white noise. The main result shows that under mild conditions, for a xxed system the gap between the H 2 and g norms can be made arbitrarily small. Motivated by these results it has been argued that the DD . Wg norm provides a useful tool for analyzing robust H 2 controllers, specially since in this context LMI-based necessary and su$cient conditions for robust performance are available. Unfortunately, as we show here with an example involving a very simple plant, the worst case DD . DD W m g norm can be conservative by at least a factor of Jm (where m denotes the dimension of the exogenous signal) for the original robust H 2 problem. Moreover, the same example shows that competing state-space based bounds also exhibit a similar degree of conservatism. Thus, at this point the problem of "nding non-conservative bounds on the worst H 2 norm under LTI or slowly-varying LTV perturbations still remains open. ( 1999 Elsevier Science Ltd. All rights reserved.