# Data-driven modeling of linear dynamical systems with quadratic output in the AAA framework

arXiv: https://arxiv.org/abs/2102.13487 · HTML: https://mlsanity.com/paper/2102.13487/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Feb 2021.

## Built on by (most cited first, 1 of 1)

- [A Deep State-Space Model Compression Method using Upper Bound on Output Error](https://mlsanity.com/paper/2510.14542/) (2025)

## Abstract (arXiv)

We extend the AAA (Adaptive-Antoulas-Anderson) algorithm to develop a data-driven modeling framework for linear systems with quadratic output (LQO). Such systems are characterized by two transfer functions: one corresponding to the linear part of the output and another one to the quadratic part. We first establish the joint barycentric representations and the interpolation theory for the two transfer functions of LQO systems. This analysis leads to the proposed AAA-LQO algorithm. We show that by interpolating the transfer function values on a subset of samples together with imposing a least-squares minimization on the rest, we construct reliable data-driven LQO models. Two numerical test cases illustrate the efficiency of the proposed method.