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On alpha- and D-negative imaginary systems

机译：在alpha和D负虚构系统上

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摘要

This paper is concerned with alpha- and D-negative imaginary systems. The definition of alpha-negative imaginary transfer functions is firstly introduced. Then, the relationship between negative imaginary and alpha-negative imaginary transfer functions is studied. By means of the generalised inverse, an alpha-negative imaginary lemma is proposed to test the alpha-negative imaginary property of transfer functions. Also, a necessary and sufficient condition is provided for the alpha-stability of interconnection of negative imaginary systems. A state-feedback controller design condition is established such that the resulting system is alpha-negative imaginary. Moreover, the concept of alpha-negative imaginary transfer functions is extended to that of D-negative imaginary transfer functions. Finally, the developed results are illustrated by numerical examples.
机译：本文涉及α负和D负虚构系统。首先介绍了α负虚传递函数的定义。然后，研究了负虚数和α-负虚数传递函数之间的关系。通过广义逆，提出了α负虚引理来检验传递函数的α负虚构性质。而且，为负虚构系统的互连的α稳定性提供了必要和充分的条件。建立状态反馈控制器设计条件，以使生成的系统为alpha负虚数。此外，α-负虚传递函数的概念被扩展到D-负虚传递函数的概念。最后，通过数值算例说明了开发结果。

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