  Linearization based controllers for incompressible flows have been proven to
work in theory and in simulations. To realize such a controller numerically,
the infinite dimensional system has to be linearized and discretized. The
unavoidable consistency errors add a small but critical uncertainty to the
controller model which will likely make it fail, especially when an observer is
involved. Standard robust controller designs can compensate small uncertainties
if they can be qualified as a coprime factor perturbation of the plant. We show
that for the linearized Navier-Stokes equations, a linearization error can be
expressed as a coprime factor perturbation and that this perturbation smoothly
depends on the size of the linearization error. In particular, improving the
linearization makes the perturbation smaller so that, eventually, standard
robust controller will stabilize the system.
