  A promising step from linear towards nonlinear data-driven control is via the
design of controllers for linear parameter-varying (LPV) systems, which are
linear systems whose parameters are varying along a measurable scheduling
signal. However, the interplay between uncertainty arising from corrupted data
and the parameter-varying nature of these systems impacts the stability
analysis, and limits the generalization of well-understood data-driven methods
for linear time-invariant systems. In this work, we decouple this interplay
using a recently developed variant of the Fundamental Lemma for LPV systems and
the viewpoint of data-informativity, in combination with biquadratic Lyapunov
forms. Together, these allow us to develop novel linear matrix inequality
conditions for the existence of scheduling-dependent Lyapunov functions,
incorporating the intrinsic nonlinearity. Appealingly, these results are stated
purely in terms of the collected data and bounds on the noise, and they are
computationally favorable to check.
