Enclosing the behavior of a hybrid automaton up to and beyond a Zeno point

Michal Konečný, Walid Taha, Ferenc A. Bartha, Jan Duracz, Adam Duracz*, Aaron D. Ames

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Even simple hybrid automata like the classic bouncing ball can exhibit Zeno behavior. The existence of this type of behavior has so far forced a large class of simulators to either ignore some events or risk looping indefinitely. This in turn forces modelers to either insert ad-hoc restrictions to circumvent Zeno behavior or to abandon hybrid automata. To address this problem, we take a fresh look at event detection and localization. A key insight that emerges from this investigation is that an enclosure for a given time interval can be valid independent of the occurrence of a given event. Such an event can then even occur an unbounded number of times. This insight makes it possible to handle some types of Zeno behavior. If the post-Zeno state is defined explicitly in the given model of the hybrid automaton, the computed enclosure covers the corresponding trajectory that starts from the Zeno point through a restarted evolution.

Original languageEnglish
Pages (from-to)1-20
Number of pages20
JournalNonlinear Analysis : Hybrid Systems
Early online date2 Dec 2015
Publication statusPublished - May 2016

Bibliographical note

© 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Funding: US National Science Foundation (awards NSF-CPS-1136099/1136104); Swedish Knowledge Foundation (KK) and the Center for Researchon Embedded Systems (CERES) (grant 20100314); and EPSRC (grant EP/C01037X/1).


  • hybrid automata
  • hybrid systems
  • rigorous computations
  • validated numerics
  • Zeno behavior


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