A constructive solution to the sub-optimal Hankel norm approximation problem for a class of infinite-dimensional systems

In this paper we present an overview/tutorial of the existing results and a constructive solution for the suboptimal Hankel norm approximation problem for the Wiener class of infinite-dimensional systems. The presented approach is based on frequency domain techniques. The construction of a solution uses a recent result on the continuity of the J-spectral factorization in the Wiener norm. The Wiener class of systems is large enough to include many infinite-dimensional matrix-valued transfer functions used in mathematical modeling of different areas applications such as optimal control, prediction, physics-based modeling (to mention only a few). Therefore we believe that our approach should be of interest not only for systems theorists but also for control engineers when dealing with applications using infinite-dimensional system models and their approximations.