Polygonal hybrid systems are a subclass of planar hybrid
automata which can be represented by piecewise constant differential
inclusions. Here, we identify and compute an important object of such
systems’ phase portrait, namely invariance kernels. An invariant set is a
set of initial points of trajectories which keep rotating in a cycle forever
and the invariance kernel is the largest of such sets. We show that this
kernel is a non-convex polygon and we give a non-iterative algorithm for
computing the coordinates of its vertices and edges. Moreover, we present
a breadth-first search algorithm for solving the reachability problem for
such systems. Invariance kernels play an important role in the algorithm.peer-reviewe
