On Reachability for Hybrid Automata over Bounded Time
  This paper investigates the time-bounded version of the reachability problem for hybrid automata. This problem asks whether a given hybrid automaton can reach a given target location within T time units, where T is a constant rational value. We show that, in contrast to the classical (unbounded) reachability problem, the timed-bounded version is decidable for rectangular hybrid automata provided only non-negative rates are allowed. This class of systems is of practical interest and subsumes, among others, the class of stopwatch automata. We also show that the problem becomes undecidable if either diagonal constraints or both negative and positive rates are allowed. 
Thomas Brihaye and Laurent Doyen and Gilles Geeraerts and Jo\"el   Ouaknine and Jean-Fran\c{c}ois Raskin and James Worrell
cs.LO