{"ID":2826159,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.19160","arxiv_id":"2512.19160","title":"Rapid stabilization of the heat equation with localized disturbance","abstract":"This paper studies the rapid stabilization of a multidimensional heat equation in the presence of an unknown spatially localized disturbance. A novel multivalued feedback control strategy is proposed, which synthesizes the frequency Lyapunov method (introduced by Xiang [41]) with the sign multivalued operator. This methodology connects Lyapunov-based stability analysis with spectral inequalities, while the inclusion of the sign operator ensures robustness against the disturbance. The closed-loop system is governed by a differential inclusion, for which well-posedness is proved via the theory of maximal monotone operators. This approach not only guarantees exponential stabilization but also circumvents the need for explicit disturbance modeling or estimation.","short_abstract":"This paper studies the rapid stabilization of a multidimensional heat equation in the presence of an unknown spatially localized disturbance. A novel multivalued feedback control strategy is proposed, which synthesizes the frequency Lyapunov method (introduced by Xiang [41]) with the sign multivalued operator. This met...","url_abs":"https://arxiv.org/abs/2512.19160","url_pdf":"https://arxiv.org/pdf/2512.19160v1","authors":"[\"Patricio Guzmán\",\"Hugo Parada\",\"Christian Calle-Cárdenas\"]","published":"2025-12-22T08:55:32Z","proceeding":"eess.SY","tasks":"[\"eess.SY\",\"math.AP\",\"math.OC\"]","methods":"[]","has_code":false}