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.