Beyond Carleman Linearization of Nonlinear Dynamical System: Insights from a Case Study
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914150152667136 |
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| author | Chen, Panpan Motee, Nader Sun, Qiyu |
| author_facet | Chen, Panpan Motee, Nader Sun, Qiyu |
| contents | Nonlinear dynamical systems are widely encountered in various scientific and engineering fields. Despite significant advances in theoretical understanding, developing complete and integrated frameworks for analyzing and designing these systems remains challenging, which underscores the importance of efficient linearization methods. In this paper, we introduce a general linearization framework with emphasis on Carleman linearization and Carleman-Fourier linearization. A detailed case study on finite-section approximation to the lifted infinite-dimensional dynamical system is provided for the dynamical system with its governing function being a trigonometric polynomial of degree one. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_07805 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Beyond Carleman Linearization of Nonlinear Dynamical System: Insights from a Case Study Chen, Panpan Motee, Nader Sun, Qiyu Dynamical Systems Systems and Control Nonlinear dynamical systems are widely encountered in various scientific and engineering fields. Despite significant advances in theoretical understanding, developing complete and integrated frameworks for analyzing and designing these systems remains challenging, which underscores the importance of efficient linearization methods. In this paper, we introduce a general linearization framework with emphasis on Carleman linearization and Carleman-Fourier linearization. A detailed case study on finite-section approximation to the lifted infinite-dimensional dynamical system is provided for the dynamical system with its governing function being a trigonometric polynomial of degree one. |
| title | Beyond Carleman Linearization of Nonlinear Dynamical System: Insights from a Case Study |
| topic | Dynamical Systems Systems and Control |
| url | https://arxiv.org/abs/2511.07805 |