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Linearization based controllers for incompressible flows have been proven towork in theory and in simulations. To realize such a controller numerically,the infinite dimensional system has to be linearized and discretized. Theunavoidable consistency errors add a small but critical uncertainty to thecontroller model which will likely make it fail, especially when an observer isinvolved. Standard robust controller designs can compensate small uncertaintiesif they can be qualified as a coprime factor perturbation of the plant. We showthat for the linearized Navier-Stokes equations, a linearization error can beexpressed as a coprime factor perturbation and that this perturbation smoothlydepends on the size of the linearization error. In particular, improving thelinearization makes the perturbation smaller so that, eventually, standardrobust controller will stabilize the system.

Convergence of Coprime Factor Perturbations for Robust Stabilization of Oseen Systems