无损负虚性质的部分分式展开及一个广义无损负虚引理
Partial-fraction Expansion of Lossless Negative Imaginary Property and A Generalized Lossless Negative Imaginary Lemma
摘要：
本文研究了无耗负虚系统的一种部分分式展开式，通过允许极点在零点，给出了一个广义无耗负虚引理。首先给出了系统为非真无耗负虚部的充要条件，并研究了无耗负虚部性质的小部分分式展开。其次，根据子分解的性质，建立了无损正实系统与无损负虚系统之间两种不同的新关系。第三，根据其中一个关系，通过允许极点在零，得到了一个关于最小状态空间实现的广义无损负虚引理。本文还研究了无耗负虚系统的一些重要性质，并提供了三个数值例子来说明所发展的理论
英文摘要：
This paper studies a partial-fraction expansion for lossless negative imaginary systems and presents a generalized lossless negative imaginary lemma by allowing poles at zero. First, a necessary and sufficient condition for a system to be non-proper lossless negative imaginary is developed, and a minor partial-fraction expansion of lossless negative imaginary property is studied. Second, according to the minor decomposition properties, two different and new relationships between lossless positive real and lossless negative imaginary systems are established. Third, according to one of the relationships, a generalized lossless negative imaginary lemma in terms of a minimal state-space realization is derived by allowing poles at zero. Some important properties of lossless negative imaginary systems are also studied in this paper, and three numerical examples are provided to illustrate the developed theory
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