Two Strings with a Dynamic Interior Mass: A Feedback Control Design with Guaranteed Exponential Decay
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912484017831936 |
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| author | Brown, Zoe Ozer, Ahmet Ozkan |
| author_facet | Brown, Zoe Ozer, Ahmet Ozkan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09558 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Two Strings with a Dynamic Interior Mass: A Feedback Control Design with Guaranteed Exponential Decay Brown, Zoe Ozer, Ahmet Ozkan Analysis of PDEs Optimization and Control 35L05, 93D15, 35B40, 93C20, 35B40 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. |
| title | Two Strings with a Dynamic Interior Mass: A Feedback Control Design with Guaranteed Exponential Decay |
| topic | Analysis of PDEs Optimization and Control 35L05, 93D15, 35B40, 93C20, 35B40 |
| url | https://arxiv.org/abs/2507.09558 |