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

共 24 条

[1] [Anonymous], 2000, Applications of Fractional Calculus in Physics
[2] Bellman R.E., 1963, Differential-Difference Equations, V6
[3] Analysis of fractional delay systems of retarded and neutral type
Bonnet, C
Partington, JR
[J]. AUTOMATICA, 2002, 38 (07) : 1133 - 1138
[4] STABILITY OF NEUTRAL SYSTEMS WITH COMMENSURATE DELAYS AND POLES ASYMPTOTIC TO THE IMAGINARY AXIS
Bonnet, Catherine
Fioravanti, Andre R.
Partington, Jonathan R.
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2011, 49 (02) : 498 - 516
[5] AN EIGENVALUE PERTURBATION APPROACH TO STABILITY ANALYSIS, PART II: WHEN WILL ZEROS OF TIME-DELAY SYSTEMS CROSS IMAGINARY AXIS?
Chen, Jie
Fu, Peilin
Niculescu, Silviu-Iulian
Guan, Zhihong
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2010, 48 (08) : 5583 - 5605
[6] AN EIGENVALUE PERTURBATION APPROACH TO STABILITY ANALYSIS, PART I: EIGENVALUE SERIES OF MATRIX OPERATORS
Chen, Jie
Fu, Peilin
Niculescu, Silviu-Iulian
Guan, Zhihong
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2010, 48 (08) : 5564 - 5582
[7] Fioravanti A. R., 2010, P 9 IFAC WORKSH TIM
[8] GU K., 2003, CONTROL ENGN SER BIR
[9] Hale JK, 2001, OPER THEORY ADV APPL, V122, P275
[10] A numerical algorithm for stability testing of fractional delay systerns
Hwang, C
Cheng, YC
[J]. AUTOMATICA, 2006, 42 (05) : 825 - 831

← 1 2 3 →