Analysis of Zeno behaviors in hybrid systems

We investigate conditions for existence of Zeno behaviors in hybrid systems. Our approach is based on a simple but crucial observation that a state of the hybrid system is reachable at a given time if and only if it is reachable at the same time in an "equivalent" continuous system that is obtained as a suitable weighted combination of the dynamic equations of the hybrid system in the different discrete configurations. Thus, instead of a difficult investigation of the rather complicated class of behaviors of the hybrid system, we examine the very simple class of behaviors of the "equivalent" continuous system.