  The Linear Parameter-Varying (LPV) framework has been introduced with the
intention to provide stability and performance guarantees for analysis and
controller synthesis for Nonlinear (NL) systems via convex methods. By
extending results of the Linear Time-Invariant framework, mainly based on
quadratic stability and $\mathcal{L}_2$-gain performance, it was assumed that
they generalize tracking and disturbance rejection guarantees for NL systems.
But as we show through examples, the notion of $\mathcal{L}_2$-gain stability
and performance is not sufficient in order to satisfy the desired guarantees in
case of tracking and disturbance rejection. We propose to solve this problem by
the application of incremental stability and performance, which does indeed
ensure these specifications. A novel approach is proposed to synthesize and
realize an LPV controller which is able to guarantee incremental stability and
performance for NL systems via convex optimization. Through examples, the
presented method is compared to standard $\mathcal{L}_2$-gain optimal LPV
controller design, showing significant performance improvements. Finally, the
approach is experimentally verified on an unbalanced disc setup, demonstrating
the shortcomings of standard $\mathcal{L}_2$-gain optimal LPV controllers.
