用关联矩阵特征值分析Petri网模型结构

通过计算由关联矩阵变换所得特殊方阵的特征值来分析Petri网模型某些重要的结构特性. 根据自由选择网、自由连接网与非自由选择网、非自由连接网关联矩阵的区别，分别用不同的方法将它们变换为同一类方阵，并用此类矩阵理论给出Petri网模型的结构有界性、守恒性、可重复性、协调性的充分条件及相关证明. 采用一个雷达工作过程建模实例详细阐述了该结构理论在实际Petri网模型分析中的应用，为关联矩阵在Petri网模型结构分析中的应用提供了一个可选择的方法.

Eigenvalues of Incidence Matrices Applied to the Analysis of Petri Net Structures

By computing eigenvalues of special square matrices derived from the incidence matrices of Petri net models, some important structural properties of Petri nets are analyzed. According to the differences between two types of nets, i.e., choice-free and link-free nets, and non-choice-free and non-link-free nets, two methods are used to transform them into the same class of square matrices. We then obtain sufficient conditions for structure boundedness, conservativeness, repetitiveness and consistency based on the theory of M-matrices. An example of radar model is given to show application in analyzing Petri net structures.