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This paper deals with data-driven stability analysis and feedbackstabillization of linear input-output systems in autoregressive (AR) form. Weassume that noisy input-output data on a finite time-interval have beenobtained from some unknown AR system. Data-based tests are then developed toanalyse whether the unknown system is stable, or to verify whether astabilizing dynamic feedback controller exists. If so, stabilizing controllersare computed using the data. In order to do this, we employ the behavioralapproach to systems and control, meaning a departure from existing methods indata driven control. Our results heavily rely on a characterization ofasymptotic stability of systems in AR form using the notion of quadraticdifference form (QDF) as a natural framework for Lyapunov functions ofautonomous AR systems. We introduce the concepts of informative data forquadratic stability and quadratic stabilization in the context of input-outputAR systems and establish necessary and sufficient conditions for theseproperties to hold. In addition, this paper will build on results on quadraticmatrix inequalties (QMIs) and a matrix version of Yakubovich's S-lemma.

A behavioral approach to data-driven control with noisy input-output data