Is there life after Zeno? Taking executions past the breaking (Zeno) point

Abstract

Understanding Zeno phenomena plays an important role in understanding hybrid systems. A natural - and intriguing - question to ask is: what happens after a Zeno point? Inspired by the construction of Filippov (1988), we propose a method for extending Zeno executions past a Zeno point for a class of hybrid systems: Lagrangian hybrid systems. We argue that after the Zeno point is reached, the hybrid system should switch to a holonomically constrained dynamical system, where the holonomic constraints are based on the unilateral constraints on the configuration space that originally defined the hybrid system. These principles are substantiated with a series of examples.