摘要：Geometric-Zeno behaviour is a highly challenging problem in the analysis (including simulation) of hybrid systems. Geometric-Zeno can be defined as an infinite number of discrete mode switches in a finite time interval. Typically, for hybrid models exhibiting geometric-Zeno, the numerical simulation either halts or produces false results, because an infinite number of discrete events occur in a given simulation time-step. In this paper, we provide formal methods for regularization of geometric-Zeno behaviour by using a non-standard analysis. In particular, we provide formal conditions for the existence of geometric-Zeno in hybrid systems, and we propose methods to allow geometric-Zeno executions to be continued beyond geometric-Zeno limit points. The concepts are illustrated with a case study throughout the paper.
