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Minimal positive realizations of transfer functions with positive real poles

机译:带有正实极点的传递函数的最小正实现

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摘要

A standard result of linear-system theory states that a SISO rational nth-order transfer function always has an nth-order realization. In some applications, one is interested in having a realization with nonnegative entries (i.e., a positive system) and it is known that a positive system may not be minimal in the usual sense. In this paper, we give an explicit necessary and sufficient condition for a third-order transfer function with distinct real positive poles to have a third-order positive realization. The proof is constructive so that it is straightforward to obtain a minimal positive realization.
机译:线性系统理论的标准结果表明,SISO有理n阶传递函数始终具有n阶实现。在某些应用中,人们对用非负项(即,正系统)实现很感兴趣,并且众所周知,在通常意义上,正系统可能不是最小的。在本文中,我们给出了具有明显实正极的三阶传递函数具有三阶正实现的明确必要和充分条件。该证明是有建设性的,因此很容易获得最小的肯定实现。

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