IJPAM: Volume 96, No. 3 (2014)

THE MODELING AND STABILITY PROBLEM
FOR A COMMUNICATION CHANNEL SYSTEM
WITH TRANSMITTER BREAKDOWN

Zvi Retchkiman Königsberg
Instituto Politecnico Nacional, CIC
Mineria 17-2, Col. Escandon, Mexico D.F. 11800, MEXICO


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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DOI: 10.12732/ijpam.v96i3.7 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 96
Issue: 3
Pages: 363 - 376


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