ℋ2 Optimal model reduction of linear dynamical systems

In this paper we consider the ℋ₂ optimal model reduction problem which has important applications in system approximation and has received considerable attention in the literature. An important link between special cases of this problem and rational interpolation using Krylov projection methods has been recently established. We use this link to derive a solution in the special case when the original system is single input single output (SISO) and the approximation has first order. We also indicate extensions to higher order approximations. Finally, we give a few examples to illustrate our procedure.