Preconditioning of transfer matrices: bounding the frequency dependent structured singular value

The precondition of matrices by diagonal sealing is a useful tool for bounding the structured singular value. Although the constant matrix case has been well studied, comparatively little is known about the behavior of the scaling matrices as a function of frequency. In this paper 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 Frobenius-norm of a scaled transfer matrix