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arXiv · 2604.05255

Hybrid Systems as Coalgebras: Lyapunov Morphisms for Zeno Stability

Joe Moeller·Aaron D. Ames
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Abstract

Hybrid dynamical systems exhibit a diverse array of stability phenomena, each currently addressed by separate Lyapunov-like results. We show that these results are all instances of a single theorem: a Lyapunov function is a morphism from a hybrid system into a simple stable target system $\sigma$, and different stability notions such as Lyapunov stability, asymptotic stability, exponential stability, and Zeno stability correspond to different choices of $\sigma$. This unification is achieved by expressing hybrid systems as coalgebras of an endofunctor $\mathcal H$ on a category $\mathsf{Chart}$ that naturally blends continuous and discrete dynamics. Instantiating a general categorical Lyapunov theorem for coalgebras to this setting results in new Lypaunov-like conditions for the stability of Zeno equilibria and the existence of Zeno behavior in hybrid systems.

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BibTeXRIS

Joe Moeller, Aaron D. Ames. 2026-04-06. Hybrid Systems as Coalgebras: Lyapunov Morphisms for Zeno Stability. https://arxiv.org/abs/2604.05255

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