一种基于线性矩阵不等式的广义负虚系统引理

A Descriptor Negative Imaginary Systems Lemma Based on Linear Matrix Inequality

文章基于系统的最小状态空间实现,拓展了广义负虚系统的辨识定理。首先,分析广义负虚系统与广义正实系统的关系,得到两者之间的变换条件;其次,给出了辨识广义负虚系统的充分性条件,文章给出的辨识条件与已有的结论相比,允许广义系统存在脉冲。最后,通过数值例子验证本文理论的正确性与有效性。

This paper is concerned with extending negative imaginary lemmas to descriptor systems without impulse-free assumption. Firstly, the previous relationship between descriptor negative imaginary systems and descriptor positive real systems is analyzed. Secondly, sufficient conditions are derived for testing descriptor negative imaginary systems and descriptor lossless negative imaginary systems based on minimal state-space realization. Finally, the validity of the developed lemmas is illustrated by two numerical examples.