On the calculation of transfer function of timed event Petri nets

In this paper, a method for the calculation of transfer function of timed event graphs is developed. The transfer function has form of a formal series in one or two formal variables. The knowledge of this formal series plays a crucial role in the max-plus system theory. Namely, it is very important in the investigation of the problem of controllability of a system, because it provides the input-output relation as an equation in the dioid of formal series. The direct approach to this calculation requires the computation of a star operation of a matrix with entries in this dioid which seems to be difficult for matrices of large dimensions. This is why the authors propose another approach using only the max-plus modelling of a system. The authors have considered the multivariable case with several input and output transitions. The authors can obtain the transfer function as the output corresponding to a special control. To illustrate this approach the authors give two examples. The purpose of the first one is to compare different approaches to this problem, whereas the second one may serve as an application. The authors use their approach to determine the transfer function of a manufacturing system