Optimal $\mathcal{H}_{2}$ model approximation based on multiple input/output delays systems
For control theorists, it provides a theoretical extension of H2 model reduction to delay systems, but the contribution is incremental as it generalizes known results without demonstrated practical advantage.
The paper derives optimality conditions for H2 approximation of transfer functions with input/output delays, extending tangential interpolation to delay systems, and proposes a two-stage algorithm. No numerical results are reported.
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.