论文标题
正真实奇数矩阵函数的凸变锥结构
The convex invertible cone structure of positive real odd rational matrix functions
论文作者
论文摘要
正真实的奇数矩阵函数（通常称为实际无损矩阵函数）在多端口电气系统中的许多应用中都起着重要作用。在本文中，我们介绍了在多端口设置中的标量，单端口案例的一些已知结果。具体而言，我们确定了研究良好的部分分数公式的必要条件，以表示在正真实奇数矩阵函数类别中的函数，并明确的最小状态空间实现该函数的逆（入学）的最小状态空间实现公式，这本身也是一个正真实的奇数矩阵函数。这样做，使我们能够从标量案例中提供一个部分类似物 - 零交织行为。
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.
