In this work, the modeling and stability problem for a communication network system is addressed.\nThe communication network system consists of a transmitter which sends messages to a\nreceiver. The proposed model considers two possibilities. The first one, that messages are successfully\nreceived, while in the second one, during the sending process the transmitter breaks\ndown and as a result the message does not reach the receiver. Timed Petrinets is the mathematical\nand graphical modeling technique utilized. Lyapunov stability theory provides the required tools\nneeded to aboard the stability problem. Employing Lyapunov methods, a sufficient condition for\nstabilization is obtained. It is shown that it is possible to restrict the communication network system\nstate space in such a way that boundedness is guaranteed. However, this restriction results to\nbe vague. This inconvenience is overcome by considering a specific recurrence equation, in the\nmax-plus algebra, which is assigned to the timed Petri net graphical model.
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