Negative imaginary lemmas for improper descriptor systems

IF 3.7 3区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Journal of The Franklin Institute-engineering and Applied Mathematics Pub Date : 2025-04-17 DOI:10.1016/j.jfranklin.2025.107690

Xiaolu Liu , Meiqi Gao , Liu Liu , Naifeng Gan

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引用次数: 0

Abstract

This paper studies the negative imaginary property for improper descriptor systems. Firstly, it is demonstrated that a descriptor system with a negative imaginary transfer function cannot be impulse-free, that is, the negative imaginary transfer function is improper. Then some necessary conditions and sufficient conditions are established to characterize the negative imaginary property of improper descriptor systems based on the quasi-Weierstrass form. Furthermore, the lossless negative imaginary property of improper descriptor systems is derived by the relationship between the lossless positive realness and the lossless negative imaginariness. Several examples are given to illustrate the obtained results. In addition, this paper presents a generalized Kalman–Yakubovich–Popov lemma for the negative imaginary property of descriptor systems, which is achieved independently of the relationship between positive realness and negative imaginariness.

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反常广义系统的负虚引理

本文研究了反常广义系统的负虚数性质。首先，证明了具有负虚传递函数的广义系统不可能是无脉冲的，即负虚传递函数是不合适的。然后建立了基于拟weierstrass形式的广义系统的负虚数性质的充分必要条件。进一步，利用广义系统的无损正实性与无损负虚性之间的关系，导出了广义系统的无损负虚性。给出了几个例子来说明所得结果。此外，本文给出了广义系统负虚性的一个广义kalman - yakubovitch - popov引理，该引理是独立于正实性与负虚性之间的关系而得到的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of The Franklin Institute-engineering and Applied Mathematics 工程技术-工程：电子与电气

CiteScore

7.30

自引率

14.60%

发文量

586

审稿时长

6.9 months

期刊介绍： The Journal of The Franklin Institute has an established reputation for publishing high-quality papers in the field of engineering and applied mathematics. Its current focus is on control systems, complex networks and dynamic systems, signal processing and communications and their applications. All submitted papers are peer-reviewed. The Journal will publish original research papers and research review papers of substance. Papers and special focus issues are judged upon possible lasting value, which has been and continues to be the strength of the Journal of The Franklin Institute.