"A Novel Frequency-Domain Approach for the Exact Range of Imaginary Spe" by Chengzhi Yuan, Shuang Song et al.

Mechanical, Industrial & Systems Engineering Faculty Publications

Title

A Novel Frequency-Domain Approach for the Exact Range of Imaginary Spectra and the Stability Analysis of LTI Systems With Two Delays

Authors

Chengzhi Yuan, University of Rhode IslandFollow
Shuang Song
Qingbin Gao
Hamid Reza Karimi
Libor Pekar
Shenghui Guo

Document Type

Article

Date of Original Version

2-17-2020

Department

Mechanical, Industrial and Systems Engineering

Abstract

This paper presents a novel frequency-domain approach to reveal the exact range of the imaginary spectra and the stability of linear time-invariant systems with two delays. First, an exact relation, i.e., the Rekasius substitution, is used to replace the exponential term caused by the delays in order to transform the transcendental characteristic equation to a quasi-polynomial. Second, this quasi-polynomial is uniquely tackled by our proposed Dixon resultant and discriminant theory, leading to the elimination of delay-related elements and the revelation of the exact range of the frequency spectra of the original system of interest. Then, by sweeping the frequency over this obtained range, the stability switching curves are declared exhaustively. Last, we deploy the cluster treatment of characteristic roots (CTCR) paradigm to reveal the exact and complete stability map. The proposed methodologies are tested and verified by a numerical method called Quasi-Polynomial mapping-based Root finder (QPmR) over an example case.

Citation/Publisher Attribution

C. Yuan, S. Song, Q. Gao, H. R. Karimi, L. Pekar and S. Guo, "A Novel Frequency-Domain Approach for the Exact Range of Imaginary Spectra and the Stability Analysis of LTI Systems With Two Delays," in IEEE Access, vol. 8, pp. 36595-36601, 2020.