Hybrid systems expressed as coalgebras allow all standard Lyapunov stability results plus new conditions for Zeno equilibria to be instances of a single morphism theorem.
Lynch, Seth Hutchinson, George A Kantor, and Wolfram Burgard.Principles of robot motion: theory, algorithms, and implementations
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Hybrid Systems as Coalgebras: Lyapunov Morphisms for Zeno Stability
Hybrid systems expressed as coalgebras allow all standard Lyapunov stability results plus new conditions for Zeno equilibria to be instances of a single morphism theorem.