Zeno hybrid systems

The interacting continuous and discrete dynamics in hybrid systems may lead to Zeno executions, which are solutions of the system having infinitely ma ny discrete transitions in finite time. Although physical systems do not sh ow Zeno behaviour, models of real systems may be Zeno due to modelling abst raction. It is hard to analyse such models with the existing theory. Since abstraction is an important tool in the hierarchical design of hybrid syste ms, one would like to determine when it may lead to Zeno models. Zeno hybri d systems are studied in detail in the paper. Necessary and sufficient cond itions for the existence of Zeno executions are given. The Zeno set is intr oduced as the omega limit set of a Zeno execution. Properties of the Zeno s et are derived for a fairly large class of hybrid systems. Copyright 2001 ( C) John Wiley & Sons, Ltd.