Distribution of Roots of Quasi-Polynomials of Neutral Type and Its Application-Part I: Determination of the Number of Roots and Hurwitz Stability Criteria

• 成果类型: Article
• 署名作者: Wang, Honghai; Han, Qing-Long
• 署名单位: Northeastern University - China; Swinburne University of Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3300348
• 发表日期: 2024
• 页码: 2979-2994
• 关键词: Stability criteria; Linear systems; DELAYS; Delay effects; Eigenvalues and eigenfunctions; Behavioral sciences; Numerical stability; Commensurate delays; Hurwitz stability criteria; linear time-invariant system; quasi-polynomial; distribution of roots

摘要

This article proposes several criteria for the distribution of roots of quasi-polynomials of neutral type with complex coefficients. Compared with Pontryagin's results, the derived criteria can be numerically implemented because the interval of the frequency for analyzing the behavior of the quasi-polynomial can be determined. Moreover, some Hurwitz stability criteria to judge whether all the roots of the quasi-polynomials are in the open left-half complex plane are provided. These Hurwitz stability criteria can be employed to analyze the stability of linear time-invariant systems with commensurate delays. It should be pointed out that on the one hand, the derived criteria are general since quasi-polynomials of retarded type and quasi-polynomials with real coefficients are their special cases. On the other hand, the conditions in Hurwitz stability criteria are all necessary and sufficient. Furthermore, as a special case, several criteria for the distribution of roots of the quasi-polynomials with real coefficients are presented. For the proposed criteria, this article provides some examples to illustrate the implementation and presents the detailed analysis and proofs.