Categorical Lyapunov Theory II: Stability of Systems
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910973280911360 |
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| author | Ames, Aaron D. Mattenet, Sébastien Moeller, Joe |
| author_facet | Ames, Aaron D. Mattenet, Sébastien Moeller, Joe |
| contents | Lyapunov's theorem provides a foundational characterization of stable equilibrium points in dynamical systems. In this paper, we develop a framework for stability for F-coalgebras. We give two definitions for a categorical setting in which we can study the stability of a coalgebra for an endofunctor F. One is minimal and better suited for concrete settings, while the other is more intricate and provides a richer theory. We prove a Lyapunov theorem for both notions of setting for stability, and a converse Lyapunov theorem for the second. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_22968 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Categorical Lyapunov Theory II: Stability of Systems Ames, Aaron D. Mattenet, Sébastien Moeller, Joe Dynamical Systems Systems and Control Category Theory 18M35, 93D05, 93D30, 37B25, 37C75 Lyapunov's theorem provides a foundational characterization of stable equilibrium points in dynamical systems. In this paper, we develop a framework for stability for F-coalgebras. We give two definitions for a categorical setting in which we can study the stability of a coalgebra for an endofunctor F. One is minimal and better suited for concrete settings, while the other is more intricate and provides a richer theory. We prove a Lyapunov theorem for both notions of setting for stability, and a converse Lyapunov theorem for the second. |
| title | Categorical Lyapunov Theory II: Stability of Systems |
| topic | Dynamical Systems Systems and Control Category Theory 18M35, 93D05, 93D30, 37B25, 37C75 |
| url | https://arxiv.org/abs/2505.22968 |