Reduction of timed hybrid systems

We consider a class of hybrid dynamical systems and obtain conditions under which the behavior of these systems can be reduced to a finite state automaton. Specifically, we consider timed automata with more general enabling regions coupling the continuous and discrete dynamics than those previously considered. We provide a necessary condition for the existence of a finite state reduction, together with examples showing that this condition is not sufficient. We then give two sufficient conditions that provide a large class of systems with general enabling regions which admit finite reductions.