### Abstract

Original language | American English |
---|---|

Pages (from-to) | 497-508 |

Number of pages | 446 |

Journal | Neural, Parallel and Scientific Computations |

State | Published - 1 Jan 2014 |

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**The modeling and stability problem for a communication network system.** / Konigsberg, Zvi Retchkiman.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - The modeling and stability problem for a communication network system

AU - Konigsberg, Zvi Retchkiman

PY - 2014/1/1

Y1 - 2014/1/1

N2 - ©Dynamic Publishers, Inc. 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 - ©Dynamic Publishers, Inc. 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.

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M3 - Article

SP - 497

EP - 508

JO - Neural, Parallel and Scientific Computations

JF - Neural, Parallel and Scientific Computations

SN - 1061-5369

ER -