Coercive ISS-Lyapunov functionals for regular infinite-dimensional systems and applications
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913821384245248 |
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| author | Marx, Swann |
| author_facet | Marx, Swann |
| contents | This paper proposes the construction of a coercive ISS-Lyapunov functional for linear regular infinite-dimensional system. Indeed, as already known, Lyapunov functionals for infinite-dimensional systems might be not coercive. Under the assumption that there exists an exactly observable output, we are able to make coercive a Lyapunov functional which is not coercive under additional regularity assumption. We discuss also about the potential applications of such a Lyapunov functional in singular perturbation theory and output regulation. The results are illustrated on a non-trivial equation, namely, the Korteweg-de Vries equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_11596 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Coercive ISS-Lyapunov functionals for regular infinite-dimensional systems and applications Marx, Swann Analysis of PDEs This paper proposes the construction of a coercive ISS-Lyapunov functional for linear regular infinite-dimensional system. Indeed, as already known, Lyapunov functionals for infinite-dimensional systems might be not coercive. Under the assumption that there exists an exactly observable output, we are able to make coercive a Lyapunov functional which is not coercive under additional regularity assumption. We discuss also about the potential applications of such a Lyapunov functional in singular perturbation theory and output regulation. The results are illustrated on a non-trivial equation, namely, the Korteweg-de Vries equation. |
| title | Coercive ISS-Lyapunov functionals for regular infinite-dimensional systems and applications |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2403.11596 |