{"title":"A review of time domain, frequency domain and stability analysis of linear complex-order systems","authors":"J. Jacob, Arti V. Tare, V. Vyawahare, V. Pande","doi":"10.1109/WIECON-ECE.2016.8009110","DOIUrl":null,"url":null,"abstract":"The main objective of this paper is to present the time domain, frequency domain and stability analysis of linear systems represented by differential equations with complex-order derivatives. The impulse and step response of three different complex-order systems have been presented numerically with the help of MATLAB. For frequency domain analysis, Bode-plots of the same three complex-order systems have been sketched. Complex-order systems have infinite numbers of complex-conjugate poles. The stability analysis of the complex-order systems has been done in two ways. Firstly, for systems to be stable, the complex-conjugate poles in the principle Riemann sheet must be in the left half plane. Secondly, the complex-order q = u + iv of the complex-order systems must be interior to an open disk in the u-v plane, for systems to be stable.","PeriodicalId":412645,"journal":{"name":"2016 IEEE International WIE Conference on Electrical and Computer Engineering (WIECON-ECE)","volume":"50 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2016 IEEE International WIE Conference on Electrical and Computer Engineering (WIECON-ECE)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/WIECON-ECE.2016.8009110","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 9
Abstract
The main objective of this paper is to present the time domain, frequency domain and stability analysis of linear systems represented by differential equations with complex-order derivatives. The impulse and step response of three different complex-order systems have been presented numerically with the help of MATLAB. For frequency domain analysis, Bode-plots of the same three complex-order systems have been sketched. Complex-order systems have infinite numbers of complex-conjugate poles. The stability analysis of the complex-order systems has been done in two ways. Firstly, for systems to be stable, the complex-conjugate poles in the principle Riemann sheet must be in the left half plane. Secondly, the complex-order q = u + iv of the complex-order systems must be interior to an open disk in the u-v plane, for systems to be stable.
本文的主要目的是给出由复阶导数微分方程表示的线性系统的时域、频域和稳定性分析。利用MATLAB对三种不同复阶系统的脉冲响应和阶跃响应进行了数值模拟。为了进行频域分析，绘制了三个复阶系统的波德图。复阶系统具有无穷多个复共轭极点。用两种方法对复阶系统进行了稳定性分析。首先，为了使系统稳定，黎曼片上的复共轭极点必须在左半平面上。其次，复阶系统的复阶q = u + iv必须在u-v平面的开盘内部，系统才能稳定。
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