  Unlike for Linear Time-Invariant (LTI) systems, for nonlinear systems, there
exists no general framework for systematic convex controller design which
incorporates performance shaping. The Linear Parameter-Varying (LPV) framework
sought to bridge this gap by extending convex LTI synthesis results such that
they could be applied to nonlinear systems. However, recent literature has
shown that naive application of the LPV framework can fail to guarantee the
desired asymptotic stability guarantees for nonlinear systems. Incremental
dissipativity theory has been successfully used in the literature to overcome
these issues for Continuous-Time (CT) systems. However, so far no solution has
been proposed for output-feedback based incremental control for the
Discrete-Time (DT) case. Using recent results on convex analysis of incremental
dissipativity for DT nonlinear systems, in this paper, we propose a convex
output-feedback controller synthesis method to ensure closed-loop incremental
dissipativity of DT nonlinear systems via the LPV framework. The proposed
method is applied on a simulation example, demonstrating improved stability and
performance properties compared to a standard LPV controller design.
