  The Linear Parameter-Varying (LPV) framework has long been used to guarantee
performance and stability requirements of nonlinear (NL) systems mainly through
the $\mathcal{L}_2$-gain concept. However, recent research has pointed out that
current $\mathcal{L}_2$-gain based LPV synthesis methods can fail to guarantee
these requirements if stabilization of a non-zero operating condition (e.g.
reference tracking, constant disturbance rejection, etc.) is required. In this
paper, an LPV based synthesis method is proposed which is able to guarantee
incremental performance and stability of an NL system even with reference and
disturbance rejection objectives. The developed approach and the current
$\mathcal{L}_2$ LPV synthesis method are compared in a simulation study of the
position control problem of a Duffing oscillator, showing performance
improvements of the proposed method compared to the current
$\mathcal{L}_2$-based approach for tracking and disturbance rejection.
