Frequency domain image of a set of linearly parametrized transfer functionst

This paper considers linearly parametrized plants whose parameters are normally distributed and addresses the problem of analyzing the image in the Nyquist plane of a set of these plants defined by a confidence ellipsoid in the parameter space. The image in the Nyquist plane of such a set of plants is made up of ellipses at each frequency. However, these two types of representation do not contain the same information. We show indeed that the probability level for the frequency domain set is generally larger than the probability for the parametric set. This phenomenon is due to the fact that the mapping between parametric and frequency domain spaces is not bijective.