A numerical method for stability windows and unstable root-locus calculation for linear fractional time-delay systems

被引：41

作者：

Fioravanti, Andre Ricardo ^{[1
]}

Bonnet, Catherine ^{[1
]}

Ozbay, Hitay ^{[2
]}

Niculescu, Silviu-Iulian ^{[3
]}

机构：

[1] Supelec, INRIA Saclay Ile de France, F-91192 Gif Sur Yvette, France

[2] Bilkent Univ, Dept Elect & Elect Engn, TR-06800 Ankara, Turkey

[3] CNRS Supelec, UMR 8506, L2S, F-91192 Gif Sur Yvette, France

来源：

AUTOMATICA | 2012年 / 48卷 / 11期

关键词：

Delay effects; Fractional systems; Neutral systems; Root-locus; EIGENVALUE PERTURBATION APPROACH;

D O I：

10.1016/j.automatica.2012.04.009

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This paper aims to provide a numerical algorithm able to locate all unstable poles, and therefore the characterization of the stability as a function of the delay, for a class of linear fractional-order neutral systems with multiple commensurate delays. We start by giving the asymptotic position of the chains of poles and the conditions for their stability for a small delay. When these conditions are met, the root continuity argument and some simple substitutions allow us to determine the locations where some roots cross the imaginary axis, providing therefore the complete characterization of the stability windows. The same method can be extended to provide the position of all unstable poles as a function of the delay. (c) 2012 Elsevier Ltd. All rights reserved.

引用

页码：2824 / 2830

页数：7

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