In this paper, the $\mathcal{ H}_{ 2}$ optimal approximation of a $n_{ y}\times{ n_{ u}}$ transfer function $\mathbf{ G}(s)$ by a finite dimensional system $\hat{ \mathbf{ H}}_{ d}(s)$ including input/output delays, is addressed. The underlying $\mathcal{ H}_{ 2}$ optimality conditions of the approximation problem are firstly derived and established in the case of a poles/residues decomposition. These latter form an extension of the tangential interpolatory conditions, presented in~\cite{ gugercin2008h_2,dooren2007} for the delay-free case, which is the main contribution of this paper. Secondly, a two stage algorithm is proposed in order to practically obtain such an approximation.
Categories: cs.SY math.DS math.NA