One of the most important problems in hybrid systems is the {\em reachability problem}. The reachability problem has been shown to be undecidable even for a subclass of {\em linear} hybrid systems. In view of this, the main focus in the area of hybrid systems has been to find {\em effective} semi-decision procedures for this problem. Such an algorithmic approach involves finding methods of computation and representation of reach sets of the continuous variables within a discrete state of a hybrid system. In this paper, after presenting a brief introduction to hybrid systems and reachability problem, we propose a computational method for obtaining the reach sets of continuous variables in a hybrid system. In addition to this, we also describe a new algorithm to over-approximate with polyhedra the reach sets of the continuous variables with linear dynamics and polyhedral initial set. We illustrate these algorithms with typical interesting examples.
Chennai Mathematical Institute, India IAI, TCG CREST, Kolkata, India（钦奈数学研究所，印度 IAI，TCG CREST，科利尔，印度）；Georgia Institute of Technology, USA University of Toronto, Canada（佐治亚理工学院，美国 蒙特利尔大学，加拿大）
