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arXiv · 2505.22968

Categorical Lyapunov Theory II: Stability of Systems

Aaron D. Ames·Sébastien Mattenet·Joe Moeller
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Abstract

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.

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BibTeXRIS

Aaron D. Ames, Sébastien Mattenet, Joe Moeller. 2025-05-29. Categorical Lyapunov Theory II: Stability of Systems. https://arxiv.org/abs/2505.22968

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