Optimal ${\mathcal{H}}_2$ model approximation based on multiple input/output delays systems

Abstract

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.

14 pages, 3 figures, submitted to Automatica Journal