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Zeno hybrid systems
Jun Zhang (University of California, Berkeley), Karl Henrik Johansson (KTH Royal Institute of Technology), John Lygeros (University of Cambridge), Shankar Sastry (University of California, Berkeley)
Abstract: Abstract The interacting continuous and discrete dynamics in hybrid systems may lead to Zeno executions, which are solutions of the system having infinitely many discrete transitions in finite time. Although physical systems do not show Zeno behaviour, models of real systems may be Zeno due to modelling abstraction. It is hard to analyse such models with the existing theory. Since abstraction is an important tool in the hierarchical design of hybrid systems, one would like to determine when it may lead to Zeno models. Zeno hybrid systems are studied in detail in the paper. Necessary and sufficient conditions for the existence of Zeno executions are given. The Zeno set is introduced as the ω limit set of a Zeno execution. Properties of the Zeno set are derived for a fairly large class of hybrid systems. Copyright 2001 © John Wiley & Sons, Ltd.