Stability analysis for a class of distributed delay systems with constant coefficients by using a frequency-sweeping approach

• Published in: IET control theory & applications Vol. 13; no. 1; pp. 87 - 95
• Main Authors: Zhang, Lu, Mao, Zhi-Zhong, Li, Xu-Guang, Niculescu, Silviu-Iulian, Çela, Arben
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 01.01.2019; Institution of Engineering and Technology
• Subjects: asymptotic behaviour analysis; authors; Automatic Control Engineering; CIRs; complete stability analysis; complete stability problem; Computer Science; constant coefficients; critical imaginary roots; critical zero roots; CZRs; delay parameter; delay systems; delays; distributed delay systems; frequency‐sweeping approach; frequency‐sweeping curves; infinitely many critical delays; invariance; invariance property; linear systems; Research Article; stability; stability property; technical issues; unified approach; technical issues; delay systems; constant coefficients; infinitely many critical delays; critical zero roots; complete stability problem; CZRs; critical imaginary roots; linear systems; frequency-sweeping curves; unified approach; invariance property; delays; distributed delay systems; complete stability analysis; asymptotic behaviour analysis; CIRs; invariance; delay parameter; stability; frequency-sweeping approach; stability property; authors; Complete stability; Asymptotic behaviour; Constant coefficients; System stability; Frequency sweeping; Stability analysis; Stability properties; Unified approach; Asymptotic analysis; Distributed delays
• ISSN: 1751-8644; 1751-8652; 1751-8652
• DOI: 10.1049/iet-cta.2018.5520

This study focuses on the stability property of a class of distributed delay systems with constant coefficients. More precisely, the authors will discuss deeper the stability analysis with respect to the delay parameter. The authors' approach will allow to give new insights in solving the so-called complete stability problem. There are three technical issues need to be studied: First, the detection of the critical zero roots (CZRs); second, the analysis of the asymptotic behaviour of such CZRs; third, the asymptotic behaviour analysis of the critical imaginary roots (CIRs) with respect to the infinitely many critical delays. They extended their recently-established frequency-sweeping approach, with which these technical issues can be effectively solved. Based on these results, a procedure was proposed, with which the complete stability analysis of such systems was accomplished systematically. Moreover, the procedure represents a unified approach: Most of the steps required by the complete stability problem may be fulfilled through observing the frequency-sweeping curves. Finally, some examples illustrate the effectiveness and advantages of the approach.