My thesis research is devoted to the study of timed continuous Petri nets systems (continuous relaxations of T-timed Petri nets), exploring three main topics:

• It is known that the marking of a timed continuous Petri net sometimes approximates the marking of a T-timed discrete Petri net, having the same structure, initial marking and timing. In this context, part of my work is devoted to study the approximation of the average marking of a stochastically timed discrete Petri net (under exponential delays) provided by the marking of the corresponding timed continuous or hybrid Petri net.

• The study of properties of timed continuous Petri nets: controllability, synthesis of controllers and the relation between liveness, boundedness and timing.

• The application of those results for controlling discrete Petri nets by using controllers originally designed for the corresponding relaxed continuous PN models. In particular, it has been explored two different cases: a stock-level control example of a kanban-based automotive asambly line, and a traffic-light periods optimization in urban traffic networks by usign hybrid Petri nets.