Is set modeling of white noise a good tool for robust H2 analysis?
✍ Scribed by Mario Sznaier; Jorge Tierno
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 174 KB
- Volume
- 36
- Category
- Article
- ISSN
- 0005-1098
No coin nor oath required. For personal study only.
✦ Synopsis
Recently, a new deterministic characterization of the H norm has been proposed, using a new norm ("" . "" 5E ), 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 and = E norms can be made arbitrarily small. Motivated by these results it has been argued that the "" . "" 5E norm provides a useful tool for analyzing robust H 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 "" . "" 5 K E norm can be conservative by at least a factor of (m (where m denotes the dimension of the exogenous signal) for the original robust H 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 norm under LTI or slowly-varying LTV perturbations still remains open.