Structural properties of positive real and reciprocal rational matrices
Structural properties of positive real and reciprocal rational matrices
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正实数和倒数有理矩阵的结构性质
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
Timo Reis
中科院分区：
文献类型：
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作者：
T. Berger;Timo Reis
我们考虑正实有理矩阵值有理函数。证明了函数的逐点核和Hermite部分的逐点核在右复半平面上是不变的。这些结果是正实矩阵分解和正交相似变换的基础。我们进一步考虑具有某种对称性的正实矩阵，这种对称性被称为“互易”。给出了倒数和正实矩阵在块正交变换下的分解。我们通过将它们应用于电路理论中的传递函数来说明我们的结果。
We consider positive real rational matrix-valued rational functions. We show that the pointwise kernel of functions as well as the pointwise kernel of the Hermitian part is constant in the right complex half plane. These results ar e the basis for a decomposition for positive real matrices und er orthogonal similarity transformation. We further consider positive real matrices which have a certain symmetry property that is known as “reciprocity”. A decomposition for reciprocal and positive real matrices under block orthogonal transformation is derived. We illustrate our results by applying them to transfer functions arising in electrical circuit theory.