Characterisation for Exponential Stability of port-Hamiltonian Systems
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866914693988220928 |
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| author | Trostorff, Sascha Waurick, Marcus |
| author_facet | Trostorff, Sascha Waurick, Marcus |
| contents | Given an energy-dissipating port-Hamiltonian system, we characterise the exponential decay of the energy via the model ingredients under mild conditions on the Hamiltonian density $\mathcal{H}$. In passing, we obtain generalisations for sufficient criteria in the literature by making regularity requirements for the Hamiltonian density largely obsolete. The key assumption for the characterisation (and thus the sufficient critera) to work is a uniform bound for a family of fundamental solutions for some non-autonomous, finite-dimensional ODEs. Regularity conditions on $\mathcal{H}$ for previously known criteria such as bounded variation are shown to imply the key assumption. Exponentially stable port-Hamiltonian systems with irregular $L_{\infty}$-densities are provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_10367 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Characterisation for Exponential Stability of port-Hamiltonian Systems Trostorff, Sascha Waurick, Marcus Analysis of PDEs Classical Analysis and ODEs 93D23, 37K40, 47D06, 34G10 Given an energy-dissipating port-Hamiltonian system, we characterise the exponential decay of the energy via the model ingredients under mild conditions on the Hamiltonian density $\mathcal{H}$. In passing, we obtain generalisations for sufficient criteria in the literature by making regularity requirements for the Hamiltonian density largely obsolete. The key assumption for the characterisation (and thus the sufficient critera) to work is a uniform bound for a family of fundamental solutions for some non-autonomous, finite-dimensional ODEs. Regularity conditions on $\mathcal{H}$ for previously known criteria such as bounded variation are shown to imply the key assumption. Exponentially stable port-Hamiltonian systems with irregular $L_{\infty}$-densities are provided. |
| title | Characterisation for Exponential Stability of port-Hamiltonian Systems |
| topic | Analysis of PDEs Classical Analysis and ODEs 93D23, 37K40, 47D06, 34G10 |
| url | https://arxiv.org/abs/2201.10367 |