4 papers
Hybrid Systems as Coalgebras: Lyapunov Morphisms for Zeno Stability
Joe Moeller, Aaron D. Ames
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…
Colored Petri Nets are Monoidal Double Functors
Jade Master, Joe Moeller
We give a characterization of colored Petri nets as monoidal double functors. Framing colored Petri nets in terms of category theory allows for canonical definitions of various wel…
Categorical Lyapunov Theory I: Stability of Flows
Aaron D. Ames, Joe Moeller, Paulo Tabuada
Lyapunov's theorem provides a fundamental characterization of the stability of dynamical systems. This paper presents a categorical framework for Lyapunov theory, generalizing stab…
Categorical Lyapunov Theory II: Stability of Systems
Aaron D. Ames, Sébastien Mattenet, Joe Moeller
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.…