  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.
