Decidability of single-rate hybrid Petri nets

We define a class of single-rate hybrid Petri nets. The continuous dynamics of these nets is such that the vector of the marking derivatives of the continuous places is constant but for a scalar factor. This class of nets can be seen as the counterpart of timed automata with skewed clocks. We prove that the reachability problem for this class can be reduced to the reachability problem of an equivalent discrete net and thus it is decidable