正实奇有理矩阵函数的凸可逆锥结构
The convex invertible cone structure of positive real odd rational matrix functions
摘要：
正实奇矩阵函数，通常被称为正实无耗矩阵函数，在多端口电气系统的许多应用中起着重要作用。在本文中，我们提出了更密切的类似物的标量，一个端口，在多端口设置的情况下，一些已知的结果。具体地说，我们确定了充要条件的研究部分分式公式表示的功能在类的正实奇矩阵函数，并明确的最小状态空间实现公式的逆（导纳）在这类函数，这本身也是一个正实奇矩阵函数。这样做，使我们能够提供一个部分模拟的极点-零交错行为从标量的情况。
英文摘要：
Positive real odd matrix functions, often referred to as positive real lossless matrix functions, play an important role in many applications in multi-port electrical systems. In this paper we present closer analogues to some of the known results for the scalar, one-port, case in the multi-port setting. Specifically, we determine necessary and sufficient conditions for the well studied partial fraction formula to represent functions in the class of positive real odd matrix functions, and explicit minimal state space realization formulas for the inverse (admittance) of a function in this class, which itself is also a positive real odd matrix function. Doing so, enables us to provide a partial analogue of the poles-zero interlacing behavior from the scalar case.
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