  The framework of linear parameter-varying (LPV) systems has shown to be a
powerful tool for the design of controllers for complex nonlinear systems using
linear tools. In this work, we derive novel methods that allow to synthesize
LPV state-feedback controllers directly from a single sequence of data and
guarantee stability and performance of the closed-loop system, without knowing
the model of the plant. We show that if the measured open-loop data from the
system satisfies a persistency of excitation condition, then the full open-loop
and closed-loop input-scheduling-state behavior can be represented using only
the data. With this representation, we formulate synthesis problems that yield
controllers that guarantee stability and performance in terms of infinite
horizon quadratic cost, generalized $\mathcal{H}_2$-norm and $\ell_2$-gain of
the closed-loop system. The controllers are synthesized by solving an SDP with
a finite set of LMI constraints. Additionally, we provide a synthesis method to
handle noisy measurement data. Competitive performance of the proposed
data-driven synthesis methods is demonstrated w.r.t. model-based synthesis that
have complete knowledge of the true system model in multiple simulation
studies, including a nonlinear unbalanced disc system.
