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Large-scale linear, time-invariant (LTI) dynamical systems are widely used tocharacterize complicated physical phenomena. We propose a two-stage algorithmto reduce the order of a large-scale LTI system given samples of its transferfunction for a target degree $k$ of the reduced system. In the first stage, amodified adaptive Antoulas--Anderson (AAA) algorithm is used to construct adegree $d$ rational approximation of the transfer function that corresponds toan intermediate system, which can be numerically stably reduced in the secondstage using ideas from the theory on Hankel norm approximation (HNA). We alsostudy the numerical issues of Glover's HNA algorithm and provide a remedy forits numerical instabilities. A carefully computed rational approximation ofdegree $d$ gives us a numerically stable algorithm for reducing an LTI system,which is more efficient than SVD-based algorithms and more accurate thanmoment-matching algorithms.

Leveraging the Hankel norm approximation and block-AAA algorithms in reduced order modeling