On the Equivalence between Similarity and Non-Similarity Scaling in Robustness Analysis

In the analysis of multivariable systems in the presence of structured uncertainties, similarity scaling and non-similarity scaling techniques have been independently proposed as methods for obtaning nonconservative robustness measures. In order to fully exploit the unique advantages of each method, it is desirable to obtain the required non-similarity scaling matrices directly from the associated similarity scaling matrix, and vice versa, without the need for separate optimizations. In this paper an explicit relationship is developed between the similarity and non-similarity scaling matrices which enables the direct computation of the non-similarity scaling matrices from the similarity scaling. Several applications of the results are also presented.