Singular value decomposition of an infinite block-Hankel matrix and its applications

This paper presents a first attempt to perform the singular value decomposition of an infinite block-Hankel matrix. It is shown that singular value decomposition (SVD) of an infinite block-Hankel matrix can be reduced to the SVD of a matrix with finite dimension. The formulation is solely in terms of the coefficients of the transfer function matrix (TFM). The most of importance is that this method leads to a new formulation of L∞-optimization problems, Hankel-norm model reduction problems and a new algorithm for minimal balanced realization of multivariable systems.