An Adaptation of the AAA-Interpolation Algorithm for Model Reduction of MIMO Systems

We consider the Adaptive Antoulas-Anderson (AAA) rational interpolation algorithm recently developed by Trefethen and co-authors, which is a type of moment-matching technique for SISO system realization and model reduction. We consider variations on this algorithm that are suitable for MIMO systems. In particular, we develop state-space formulas and keep track of the state-space dimension at every step of the adaptive block-AAA algorithm, showing an unfavorable increase of the state dimension. We propose a new low-rank adaptive interpolation algorithm that addresses this shortcoming. Comparative computational results are included for the algorithms above, together with comparisons to balanced truncation.