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Optimal $\mathcal{H}_{2}$ model approximation based on multiple input/output delays systems (1511.05252v1)
Published 17 Nov 2015 in cs.SY, math.DS, and math.NA
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.