  Nonlinear feedback design via state-dependent Riccati equations is well
established but unfeasible for large-scale systems because of computational
costs. If the system can be embedded in the class of linear parameter-varying
(LPV) systems with the parameter dependency being affine-linear, then the
nonlinear feedback law has a series expansion with constant and precomputable
coefficients. In this work, we propose a general method to approximating
nonlinear systems such that the series expansion is possible and efficient even
for high-dimensional systems. We lay out the stabilization of incompressible
Navier-Stokes equations as application, discuss the numerical solution of the
involved matrix-valued equations, and confirm the performance of the approach
in a numerical example.
