Theory and computation of discrete state space decompositions for hybrid systems

We introduce and classify abstract properties such as asymptotic stabilizability and detectability for hybrid systems and we present structural decompositions of the hybrid system discrete state-space with respect to those properties. In particular, to make the verification of the abstract properties computationally tractable, we introduce appropriate subsystems of the given hybrid system, such that checking a property on these subsystems is equivalent to checking the same property on the original system. keywords: Hybrid systems, decompositions, properties, stabilizability, safety.