PRECONDITIONING OF TRANSFER-MATRICES - BOUNDING THE FREQUENCY-DEPENDENT STRUCTURED SINGULAR-VALUE

The precondition of matrices by diagonal scaling is a useful tool for bounding the structured singular value. Although the constant matrix c ase has been well studied, comparatively little is known about the beh avior of the scaling matrices as a function of frequency. In this pape r this problem is addressed by considering the optimal Frobenius-norm scaling. It is shown that, under mild assumptions, there exist stable and minimum-phase diagonal transfer matrices which minimize the Froben ius-norm of a scaled transfer matrix.