Blowing up affine hybrid systems

In this paper we construct the "blow up" of an affine hybrid system H, i.e., a new affine hybrid system Bl(H) in which H is embedded, that does not exhibit Zeno behavior. We show the existence of a bijection ϒ between periodic orbits and equilibrium points of H and Bl(H) that preserves stability; we refer to this property as P-stability equivalence.