Realization independent single time-delay dynamical model interpolation and $\mathcal{H}_2$-optimal approximation
Abstract
In this paper, the realization-free model approximation problem, as stated in \cite{mayo2007framework,beattie2012realization}, is revisited in the case where the interpolating model might be time-delay dependent. To this aim, the Loewner framework, initially settled for delay-free realization, is firstly generalized to the single delay case. Secondly, the (infinite) model approximation optimality conditions are established through the use of the Lambert functions. Finally, a numerically effective iterative scheme, named \textbf{dTF-IRKA}, similar to the \textbf{TF-IRKA} \cite{beattie2012realization}, is proposed to reach a part of the aforementioned optimality conditions. The proposed method validity and interest are assessed on different numerical examples.
Cite
@article{arxiv.1504.06457,
title = {Realization independent single time-delay dynamical model interpolation and $\mathcal{H}_2$-optimal approximation},
author = {I. Pontes Duff and C. Poussot-Vassal and C. Seren},
journal= {arXiv preprint arXiv:1504.06457},
year = {2015}
}
Comments
14 pages, 4 figures, submitted to CDC2015