Computing the McMillan degree of a transfer function matrix G requires writing G in the Smith-McMillan form or computing all of the minors of G. This becomes more difficult and computationally expensive as the dimension of G increases. This paper introduces a simple approach to compute the McMillan degree of G without the need to write G in the Smith-McMillan form and without the need to compute all of the minors of G. The presented approach requires less computations than the approaches in the literature and clarifies the relationship between the McMillan degree, the poles, and the transmission zeros of a MIMO system. We assume that the roots of the least common multiple of the denominators of the entries of G satisfy a multiplicity condition, which can be verified prior to the application of the algorithm. The proposed approach can be beneficial for systems with many inputs and many outputs.

计算传递函数矩阵G的 McMillan 度需要将G写成Smith-McMillan 形式或计算G 的所有次要。随着G的维度增加，这变得更加困难且计算成本高。本文介绍了一种计算G的 McMillan 度的简单方法，无需将G写成Smith-McMillan 形式，也无需计算G 的所有次要. 所提出的方法比文献中的方法需要更少的计算，并阐明了 MIMO 系统的 McMillan 度、极点和传输零点之间的关系。我们假设G的条目的分母的最小公倍数的根满足重数条件，这可以在应用算法之前进行验证。所提出的方法对于具有许多输入和许多输出的系统可能是有益的。