Well-posedness of boundary control systems and application to ISS for coupled heat equations with boundary disturbances and delays
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866910050643083264 |
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| author | Gantouh, Yassine El Zheng, Jun Zhu, Guchuan |
| author_facet | Gantouh, Yassine El Zheng, Jun Zhu, Guchuan |
| contents | This paper studies the existence of solutions and, in particular, the well-posedness of a class of boundary control systems. Our main result provides explicit and verifiable conditions on the system data that guarantee continuous dependence of solutions on the initial data and $L^p$-inputs. The proof relies on a new boundedness estimate for the input/output maps of linear time-invariant infinite-dimensional systems with unbounded control and observation operators. The developed technique is applied to derive specific conditions for the exponential input-to-state stability of boundary-coupled heat equations with boundary disturbances and time-delays. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_12029 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Well-posedness of boundary control systems and application to ISS for coupled heat equations with boundary disturbances and delays Gantouh, Yassine El Zheng, Jun Zhu, Guchuan Optimization and Control This paper studies the existence of solutions and, in particular, the well-posedness of a class of boundary control systems. Our main result provides explicit and verifiable conditions on the system data that guarantee continuous dependence of solutions on the initial data and $L^p$-inputs. The proof relies on a new boundedness estimate for the input/output maps of linear time-invariant infinite-dimensional systems with unbounded control and observation operators. The developed technique is applied to derive specific conditions for the exponential input-to-state stability of boundary-coupled heat equations with boundary disturbances and time-delays. |
| title | Well-posedness of boundary control systems and application to ISS for coupled heat equations with boundary disturbances and delays |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2603.12029 |