The AAA framework for modeling linear dynamical systems with quadratic output

TL;DR

This paper introduces the AAA framework for modeling linear dynamical systems with quadratic output by defining transfer functions and extending the AAA algorithm to data-driven modeling.

Contribution

It presents a novel approach to model quadratic output systems using transfer functions and an extended AAA algorithm from data.

Findings

Effective modeling of quadratic output systems demonstrated

Transfer functions accurately describe system dynamics

Extended AAA algorithm enables data-driven system identification

Abstract

We consider linear dynamical systems with quadratic output. We first define the two transfer functions, a single-variable and a multivariate one, that fully describe the dynamics of these special nonlinear systems. Then, using the samples of these two transfer functions, we extend the AAA algorithm to model linear systems with quadratic output from data.