  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.
