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Output-based controllers are known to be fragile with respect to modeluncertainties. The standard $\mathcal{H}_{\infty}$-control theory provides ageneral approach to robust controller design based on the solution of the$\mathcal{H}_{\infty}$-Riccati equations. In view of stabilizing incompressibleflows in simulations, two major challenges have to be addressed: thehigh-dimensional nature of the spatially discretized model and thedifferential-algebraic structure that comes with the incompressibilityconstraint. This work demonstrates the synthesis of low-dimensional robustcontrollers with guaranteed robustness margins for the stabilization ofincompressible flow problems. The performance and the robustness of thereduced-order controller with respect to linearization and model reductionerrors are investigated and illustrated in numerical examples.

Robust output-feedback stabilization for incompressible flows using low-dimensional $\mathcal{H}_{\infty}$-controllers