On simulation of zeno hybrid systems

The interaction of event-driven with time-driven dynamics in hybrid systems may lead to so-called Zeno behaviour, characterized by accumulation of an infinite number of events within a finite time-interval. Although real systems are not Zeno, hybrid models may exhibit Zeno behaviour, due to modelling abstraction. Understanding this is essential for numerical simulation of hybrid systems, which may become imprecise or time-consuming. In this paper, some basic definitions from the theory of Zeno hybrid systems are firstly overviewed, together with a Simulink model of a Zeno bouncing ball model. For a Zeno water tank model, classic in the literature, a simulation approach based on fixed-step discretization of the continuous state equations is proposed.