This paper studies some useful properties of lossless negative imaginary transfer matrices for both continuous-time and discrete-time systems. Necessary and sufficient conditions are established for lossless negative imaginary systems both in frequency domain and state-space realization. Meanwhile, a minor decomposition method for lossless negative imaginary systems is proposed in terms of a partial-fraction expansion. This method is important for developing non-proper lossless negative imaginary theory in this paper by allowing poles at the origin and infinity. Two new relationships between lossless positive real and lossless negative imaginary systems are consequently established. According to these new established relationships, a generalized continuous-time lossless negative imaginary lemma and a different version of discrete-time lossless negative imaginary lemma are developed in terms of a minimal state-space realization. Several examples are provided to illustrate the main results.

本文研究了连续时间和离散时间系统的无损负虚部转移矩阵的一些有用性质。为无损负虚构系统在频域和状态空间实现中都建立了充要条件。同时，从局部分数展开的角度出发，提出了一种无损负虚构系统的小分解方法。通过使极点位于原点和无穷大处，该方法对于发展非适当的无损负虚构理论非常重要。因此建立了无损正实虚无系统之间的两个新关系。根据这些新建立的关系，从最小状态空间实现的角度，开发了广义连续时间无损负虚引理和离散时间无损负虚引理的不同版本。提供了一些示例来说明主要结果。