{"ID":2832650,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.05910","arxiv_id":"2512.05910","title":"Numerically Reliable Brunovsky Transformations","abstract":"The Brunovsky canonical form provides sparse structural representations that are beneficial for computational optimal control, yet existing methods fail to compute it reliably. We propose a technique that produces Brunovsky transformations with substantially lower construction errors and improved conditioning. A controllable linear system is first reduced to the staircase form via an orthogonal similarity transformation. We then derive a simple linear parametrization of the transformations yielding the unique Brunovsky form. Numerical stability is further enhanced by applying a deadbeat gain before computing system matrix powers and by optimizing the linear parameters to minimize condition numbers.","short_abstract":"The Brunovsky canonical form provides sparse structural representations that are beneficial for computational optimal control, yet existing methods fail to compute it reliably. We propose a technique that produces Brunovsky transformations with substantially lower construction errors and improved conditioning. A contro...","url_abs":"https://arxiv.org/abs/2512.05910","url_pdf":"https://arxiv.org/pdf/2512.05910v2","authors":"[\"Shaohui Yang\",\"Colin N. Jones\"]","published":"2025-12-05T17:45:48Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"eess.SY\"]","methods":"[]","has_code":false}