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Retchkiman, Z. (2005) Stability Theory for a Class of Dynamical Systems Modeled with Petri Nets. International Journal of Hybrid Systems, 4.

has been cited by the following article:

  • 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.