  The control of nonlinear large-scale dynamical models such as the
incompressible Navier-Stokes equations is a challenging task. The computational
challenges in the controller design come from both the possibly large state
space and the nonlinear dynamics. A general purpose approach certainly will
resort to numerical linear algebra techniques which can handle large system
sizes or to model order reduction. In this work we propose a two-folded model
reduction approach tailored to nonlinear controller design for incompressible
Navier-Stokes equations and similar PDE models that come with quadratic
nonlinearities. Firstly, we approximate the nonlinear model within in the class
of LPV systems with a very low dimension in the parametrization. Secondly, we
reduce the system size to a moderate number of states. This way, standard
robust LPV theory for nonlinear controller design becomes feasible. We
illustrate the procedure and its potentials by numerical simulations.
