Fundamental properties of hybrid automata, such as existence and uniqueness
of executions, are studied. Particular attention is devoted to Zeno hybrid
automata, which are hybrid automata that take infinitely many discrete tra
nsitions in finite time. It is shown that regularization techniques can be
used to extend the Zeno executions of these automata to times beyond the Ze
no time. Different types of regularization may, however, lead to different
extensions. A water tank control problem and a bouncing ball system are use
d to illustrate the results. (C) 1999 Elsevier Science B.V. All rights rese
rved.