{"ID":2895191,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.09558","arxiv_id":"2507.09558","title":"Two Strings with a Dynamic Interior Mass: A Feedback Control Design with Guaranteed Exponential Decay","abstract":"This paper investigates the exponential stabilization of a coupled two-string system joined by a dynamic interior mass. The combined effect of three feedback mechanisms, boundary damping from tip velocity, higher-order nodal damping from angular velocity, and lower-order nodal damping from mass velocity, is analyzed using a Lyapunov framework. Exponential stability is established unconditionally, without constraints on wave speeds or mass location, improving upon earlier results that lower-order nodal damping, as in {Hansen-Zuazua'95}, or boundary damping alone, as in {Lee-You'89}, does not ensure exponential decay without additional structural conditions. Moreover, the lower-order feedback can be removed without loss of exponential decay when combined with the other two mechanisms, via a compact perturbation argument. These results apply to hybrid systems with interior or tip mass interfaces, including overhead cranes, deep-sea cables, and fluid structure interaction. Theoretical findings are validated through numerical simulations.","short_abstract":"This paper investigates the exponential stabilization of a coupled two-string system joined by a dynamic interior mass. The combined effect of three feedback mechanisms, boundary damping from tip velocity, higher-order nodal damping from angular velocity, and lower-order nodal damping from mass velocity, is analyzed us...","url_abs":"https://arxiv.org/abs/2507.09558","url_pdf":"https://arxiv.org/pdf/2507.09558v1","authors":"[\"Zoe Brown\",\"Ahmet Ozkan Ozer\"]","published":"2025-07-13T10:03:38Z","proceeding":"math.AP","tasks":"[\"math.AP\",\"math.OC\"]","methods":"[]","has_code":false}