The Relation between the Stabilization Problem for Discrete Event Systems Modeled with Timed Petri Nets via Lyapunov Methods and Max-Plus Algebra
The Relation between the Stabilization Problem for Discrete Event Systems Modeled with Timed Petri Nets via Lyapunov Methods and Max-Plus Algebra作者机构：Instituto Politécnico Nacional CIC Mineria 17-2 Col. Escandon Mexico D.F 11800 Mexico
出 版 物：《Journal of Applied Mathematics and Physics》 (应用数学与应用物理（英文）)
年 卷 期：2015年第3卷第7期
页 面：839-845页
学科分类：1002[医学-临床医学] 100214[医学-肿瘤学] 10[医学]
主 题：Discrete Event Systems Lyapunov Methods Max-Plus Algebra Timed Petri Nets
摘 要：A discrete event system is a dynamical system whose state evolves in time by the occurrence of events at possibly irregular time intervals. Timed Petri nets are a graphical and mathematical modeling tool applicable to discrete event systems in order to represent its states evolution where the timing at which the state changes is taken into consideration. One of the most important performance issues to be considered in a discrete event system is its stability. Lyapunov theory provides the required tools needed to aboard the stability and stabilization problems for discrete event systems modeled with timed Petri nets whose mathematical model is given in terms of difference equations. By proving stability one guarantees a bound on the discrete event systems state dynamics. When the system is unstable, a sufficient condition to stabilize the system is given. It is shown that it is possible to restrict the discrete event systems state space in such a way that boundedness is achieved. However, the restriction is not numerically precisely known. 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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