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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.11194 |
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| _version_ | 1866917778443730944 |
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| author | Viscovini, Eduardo Celso |
| author_facet | Viscovini, Eduardo Celso |
| contents | For bilinear control systems in $\mathbb{R}^d$ we prove, under an accessibility hypothesis, the existence of a nontrivial compact set $D\subset\mathbb{R}^d$ satisfying $\mathcal{O}_t(D)=e^{tR}D$ for all $t>0$, where $R\in\mathbb{R}$ is a fixed constant and $\mathcal{O}_t(D)$ denotes the orbit from $D$ at time $t$. This property generalizes the trajectory of an eigenvector on a linear dynamical system, and merits such a set the name "eigenset". |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_11194 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence of eigensets on bilinear control systems Viscovini, Eduardo Celso Optimization and Control For bilinear control systems in $\mathbb{R}^d$ we prove, under an accessibility hypothesis, the existence of a nontrivial compact set $D\subset\mathbb{R}^d$ satisfying $\mathcal{O}_t(D)=e^{tR}D$ for all $t>0$, where $R\in\mathbb{R}$ is a fixed constant and $\mathcal{O}_t(D)$ denotes the orbit from $D$ at time $t$. This property generalizes the trajectory of an eigenvector on a linear dynamical system, and merits such a set the name "eigenset". |
| title | Existence of eigensets on bilinear control systems |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2409.11194 |