h2h2-norm optimal model reduction for large scale discrete dynamical MIMO systems

Modeling strategies often result in dynamical systems of very high dimension. It is then desirable to find systems of the same form but of lower complexity, whose input–output behavior approximates the behavior of the original system. Here we consider linear time-invariant discrete-time dynamical systems. The cornerstone of this paper is a relation between optimal model reduction in the h2h2-norm and (tangential) rational Hermite interpolation. First order necessary conditions for h2h2-optimal model reduction are presented for discrete Multiple-Input–Multiple-Output (MIMO) systems. These conditions suggest a specific choice of interpolation data and a novel algorithm aiming for anh2h2-optimal model reduction for MIMO systems. It is also shown that the conditions are equivalent to two known gramian-based first order necessary conditions. Numerical experiments demonstrate the approximation quality of the method.