  Output-based controllers are known to be fragile with respect to model
uncertainties. The standard $\mathcal{H}_{\infty}$-control theory provides a
general approach to robust controller design based on the solution of the
$\mathcal{H}_{\infty}$-Riccati equations. In view of stabilizing incompressible
flows in simulations, two major challenges have to be addressed: the
high-dimensional nature of the spatially discretized model and the
differential-algebraic structure that comes with the incompressibility
constraint. This work demonstrates the synthesis of low-dimensional robust
controllers with guaranteed robustness margins for the stabilization of
incompressible flow problems. The performance and the robustness of the
reduced-order controller with respect to linearization and model reduction
errors are investigated and illustrated in numerical examples.
