{"ID":2878855,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.17251","arxiv_id":"2508.17251","title":"One Equation to Rule Them All -- Part II: Direct Data-Driven Reduction and Regulation","abstract":"The Sylvester equation underpins a wide spectrum of control synthesis and systems analysis tools associated with cascade interconnections. In the preceding Part I [1] of this article, it was shown that such an equation can be reformulated using data, enabling the production of a collection of data-driven stabilisation procedures. In this second part of the article, we continue to develop the framework established in Part I to solve two important control-theoretic problems: model order reduction and output regulation. For the model order reduction problem we provide a solution from input-state measurements, from input-output measurements, and we study the effect of the noise. For the output regulation problem, we provide data-driven solutions for the static and dynamic feedback problem. The proposed designs are illustrated by means of examples.","short_abstract":"The Sylvester equation underpins a wide spectrum of control synthesis and systems analysis tools associated with cascade interconnections. In the preceding Part I [1] of this article, it was shown that such an equation can be reformulated using data, enabling the production of a collection of data-driven stabilisation...","url_abs":"https://arxiv.org/abs/2508.17251","url_pdf":"https://arxiv.org/pdf/2508.17251v1","authors":"[\"Junyu Mao\",\"Emyr Williams\",\"Thulasi Mylvaganam\",\"Giordano Scarciotti\"]","published":"2025-08-24T08:21:47Z","proceeding":"eess.SY","tasks":"[\"eess.SY\",\"math.OC\"]","methods":"[]","has_code":false}