Is set modeling of white noise a good tool for robust \({\mathcal H}_2\) analysis?
The main purpose of the paper is to indicate weak properties of an approximate set membership modelling of white noise proposed by \textit{F. Paganini} [see, e.g., IEEE Trans. Autom. Control 41, 1453-1465 (1996; Zbl 0864.93088)]. This approach is a useful tool for \(H_2\) analysis and design of systems without uncertainty. Nevertheless its use for worst case design of uncertain systems is doubtful since it leads to conservative results by a factor of square roots of the exogenous signal dimension. The authors show that the conservatism is the feature of this technique no matter whether the spectral or the state space approach is applied. As a consequence, the authors claim that the problem of obtaining convex tight bounds on the worst case \(H_2\) performance in the presence of uncertainty is not solved.
scientific article; zbMATH DE number 1394979
scientific article