On sampling continuous timed Petri nets: reachability equivalence under infinite servers semantics

This paper addresses a sampling problem for timed continuous Petri nets under infinite servers semantics. Different representations of the continuous Petri net system are given, the first two in terms of piecewise linear system and the third one, for the controlled continuous Petri nets systems, in terms of a particular linear constrained system with null dynamic matrix. The last one is used to obtain the discrete-time representation. An upper bound on sample period is given in order to preserve important information of timed continuous nets, in particular the positiveness of the markings. The reachability space of the sampled system in relation to autonomous continuous Petri nets is also studied