TY - JOUR
T1 - The modeling and stability problem for a communication network system
AU - Konigsberg, Zvi Retchkiman
N1 - Publisher Copyright:
©Dynamic Publishers, Inc.
PY - 2014/12/1
Y1 - 2014/12/1
N2 - 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 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 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.
AB - 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 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 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.
KW - Communication network system
KW - Discrete event dynamical systems
KW - Lyapunov method
KW - Max-plus algebra
KW - Timed petri nets
KW - Transmitter breakdown
UR - http://www.scopus.com/inward/record.url?scp=84921727100&partnerID=8YFLogxK
M3 - Artículo
SN - 1061-5369
VL - 22
SP - 497
EP - 508
JO - Neural, Parallel and Scientific Computations
JF - Neural, Parallel and Scientific Computations
IS - 4
ER -