Categorical Lyapunov Theory II: Stability of Systems
Dynamical Systems
2025-05-30 v1 Systems and Control
Systems and Control
Category Theory
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.
Cite
@article{arxiv.2505.22968,
title = {Categorical Lyapunov Theory II: Stability of Systems},
author = {Aaron D. Ames and Sébastien Mattenet and Joe Moeller},
journal= {arXiv preprint arXiv:2505.22968},
year = {2025}
}
Comments
33 pages