极大代数意义下矩阵的特征值问题——一类离散事件动态系统运行周期的分析

THE EIGEN-PROBLEM OF MATRIX IN MAX-ALGEBRA——ANALYSIS FOR OPERATING PERIOD OF A CLASS OF DEDS

在分析一类离散事件动态系统的运行周期及稳定性时,必须求解极大代数意义下矩阵的特征值及特征向量,这一直被认为是十分困难和繁复的工作.本文给出了求任一方阵特征值及特征向量的十分简单易行的方法以及有关的定理.

In this paper, eigen-problem of matrix in Max-algebra is discussed for analyzing the periodicity (or stability) of a class of discrete event dynamic systems (DEDS). Cohen and Karp have provided some algorithms to solve eigenvalue of matrix in Max-algebra. But these algorithms are only suitable to irreducible matrices. For reducible matrices, dominant and permanent of matrix must be calculated previously, which is very troublesome. In the paper, a new simple algorithm for determining eigenvalues and eigenvectors of a matrix in Max-algebra is presented by means of analyzing period behavior of the matrix.