TITLE:
Modeling and Stability Analysis of a Communication Network System
AUTHORS:
Zvi Retchkiman Königsberg
KEYWORDS:
Communication Network System, Transmitter Breakdown, Discrete Event Dynamical Systems, Max-Plus Algebra, Lyapunov Method, Timed Petri Nets
JOURNAL NAME:
Journal of Computer and Communications,
Vol.3 No.11,
November
19,
2015
ABSTRACT: In this work, the modeling and
stability problem for a communication network system is addressed. The
communication network system consists of a transmitter which sends messages to
a receiver. The proposed model considers two possibilities. The first one, that
messages are successfully received, while in the second one, during the sending
process the transmitter breaks down and as a result the message does not reach
the receiver. Timed Petrinets 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 network system 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.