Abstract In some applications one is interested in having a state–space realization with nonnegative matrices (positive realization) of a given transfer function and it is known that such a realization may have a dimension strictly larger than the order of the transfer function itself. Moreover, in most cases, it is desirable to have a realization with minimal dimension. Unfortunately, it is not known, to date, how to determine in general the minimum dimension of a positive realization and only lower and upper bounds to it are available. This letter provides an upper bound on the dimension of a minimal positive realization for transfer functions with simple poles. This is a considerable improvement on an earlier upper bound in which only transfer functions with real poles were considered.

中文翻译：

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离散时间系统的最小正实现维数的上限

摘要 在某些应用中，人们对具有给定传递函数的非负矩阵（正实现）的状态空间实现感兴趣，并且众所周知，这种实现的维度可能严格大于传递函数本身的阶数。此外，在大多数情况下，需要具有最小尺寸的实现。不幸的是，迄今为止，尚不知道一般如何确定正实现的最小维度，并且只有它的下限和上限可用。这封信提供了具有简单极点的传递函数的最小正实现维度的上限。这是对早期上限的相当大的改进，其中仅考虑具有实极点的传递函数。