Abstract. In this work, the modeling and stability problem for a communication channel system with transmitter breakdown is considered. Timed Petri nets is the mathematical and graphical modeling technique utilized. Lyapunov stability theory provides the required tools needed to aboard the stability problem. Employing Lyapunov methods, a sufficient condition for stabilization is obtained. It is shown that it is possible to restrict the communication channel system with transmitter breakdown state space in such a way that boundedness is guaranteed. However, this restriction results to be vague. This inconvenience is overcome by considering a specific recurrence equation, in the max-plus algebra, which is assigned to the timed Petri net graphical model.

Received: July 12, 2014

AMS Subject Classification: 08A99, 93D35, 93D99, 39A11, 08C99, 16Y60, 65F15, 05C50, 15A29, 15A33

Key Words and Phrases: communication channel system, transmitter breakdown, discrete event dynamical systems, max-plus algebra, Lyapunov method, timed Petri nets

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This work is licensed under the Creative Commons Attribution International License (CC BY).