Singular value decomposition in sensitivity minimisation for digital filters

The singular value decomposition (SVD) is used in the minimization of a previously given integral sensitivity measure. It is shown that the necessary and sufficient condition for the minimum of this measure is that the integrand, the frequency-dependent measure (FDSM), takes its minimum value with respect to the singular values of the transformation matrix T. This minimum is an attainable lower bound of the FDSM for all values of z for any transfer function. It is shown that this case corresponds to internally balanced realization (IBR) and any realization within an orthogonal transformation of the IBR.<>