TY - JOUR
T1 - The modeling and stability problem for a communication channel system with transmitter breakdown
AU - Königsberg, Zvi Retchkiman
N1 - Publisher Copyright:
© 2014 Academic Publications, Ltd.
PY - 2014
Y1 - 2014
N2 - 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.
AB - 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.
KW - Communication channel 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=84908044380&partnerID=8YFLogxK
U2 - 10.12732/ijpam.v96i3.7
DO - 10.12732/ijpam.v96i3.7
M3 - Artículo
SN - 1311-8080
VL - 96
SP - 363
EP - 376
JO - International Journal of Pure and Applied Mathematics
JF - International Journal of Pure and Applied Mathematics
IS - 3
ER -