  This paper deals with data-driven stability analysis and feedback
stabillization of linear input-output systems in autoregressive (AR) form. We
assume that noisy input-output data on a finite time-interval have been
obtained from some unknown AR system. Data-based tests are then developed to
analyse whether the unknown system is stable, or to verify whether a
stabilizing dynamic feedback controller exists. If so, stabilizing controllers
are computed using the data. In order to do this, we employ the behavioral
approach to systems and control, meaning a departure from existing methods in
data driven control. Our results heavily rely on a characterization of
asymptotic stability of systems in AR form using the notion of quadratic
difference form (QDF) as a natural framework for Lyapunov functions of
autonomous AR systems. We introduce the concepts of informative data for
quadratic stability and quadratic stabilization in the context of input-output
AR systems and establish necessary and sufficient conditions for these
properties to hold. In addition, this paper will build on results on quadratic
matrix inequalties (QMIs) and a matrix version of Yakubovich's S-lemma.
