On the equivalence between similarity and nonsimilarity scaling in robustness analysis

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