Towards Computing Phase Portraits of Polygonal Differential Inclusions

Polygonal hybrid systems are a subclass of planar hybrid automata which can be represented by piecewise constant dierential inclusions. Here, we study the problem of de ning and constructing the phase portrait of such systems. We identify various important elements of it, such as viability and controllability kernels, and propose an algorithm for computing them all. The algorithm is based on a geometric analysis of trajectories