  The versatility of data-driven approximation by interpolatory methods,
originally settled for model approximation purpose, is illustrated in the
context of linear controller design and stability analysis of irrational
models. To this aim, following an academic driving example described by a
linear partial differential equation, it is shown how the Loewner-based
interpolation may be an essential ingredient for control design and stability
analysis. More specifically, the interpolatory framework is first used to
approximate the irrational model by a rational one that can be used for
model-based control, and secondly, it is used for direct data-driven control
design, showing equivalent results. Finally, this interpolation framework is
employed for estimating the stability of the interconnection of the irrational
model with a rational controller.
