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The standard<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\mathcal {H}_{\\infty }$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msub><mml:mi>H<\/mml:mi><mml:mi>\u221e<\/mml:mi><\/mml:msub><\/mml:math><\/jats:alternatives><\/jats:inline-formula>-control theory provides a general approach to robust controller design based on the solution of the<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\mathcal {H}_{\\infty }$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msub><mml:mi>H<\/mml:mi><mml:mi>\u221e<\/mml:mi><\/mml:msub><\/mml:math><\/jats:alternatives><\/jats:inline-formula>-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.<\/jats:p>","DOI":"10.1007\/s10589-022-00359-x","type":"journal-article","created":{"date-parts":[[2022,3,9]],"date-time":"2022-03-09T09:02:47Z","timestamp":1646816567000},"page":"225-249","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Robust output-feedback stabilization for incompressible flows using low-dimensional $$\\mathcal {H}_{\\infty }$$-controllers"],"prefix":"10.1007","volume":"82","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3362-4103","authenticated-orcid":false,"given":"Peter","family":"Benner","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0228-8522","authenticated-orcid":false,"given":"Jan","family":"Heiland","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1667-4862","authenticated-orcid":false,"given":"Steffen W. 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