Stability and stabilization of fractional-order linear systems with convex polytopic uncertainties

被引：0
作者：
Jun-Guo Lu
YangQuan Chen
机构：
[1] Shanghai Jiao Tong University and Key Laboratory of System Control and Information Processing — Ministry of Education of China,Department of Automation
[2] University of California,Mechatronics, Embedded Systems and Automation (MESA) Lab. School of Engineering
来源：
Fractional Calculus and Applied Analysis | 2013年 / 16卷
关键词：
fractional-order system; convex polytopic uncertainty; robust stability; robust stabilization; linear matrix inequality (LMI); Primary 26A33; Secondary 34A08, 34D10, 93C73, 93D09, 93D21;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This paper considers the problems of robust stability and stabilization for a class of fractional-order linear time-invariant systems with convex polytopic uncertainties. The stability condition of the fractional-order linear time-invariant systems without uncertainties is extended by introducing a new matrix variable. The new extended stability condition is linear with respect to the new matrix variable and exhibits a kind of decoupling between the positive definite matrix and the system matrix. Based on the new extended stability condition, sufficient conditions for the above robust stability and stabilization problems are established in terms of linear matrix inequalities by using parameter-dependent positive definite matrices. Finally, numerical examples are provided to illustrate the proposed results.
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页码：142 / 157
页数：15
相关论文
共 59 条
  • [1] Ahn H.S.(2008)Necessary and sufficient stability condition of fractional-order interval linear systems Automatica 44 2985-2988
  • [2] Chen Y.Q.(2007)Robust stability test of a class of linear time-invariant interval fractional-order system using Lyapunov inequality Appl. Math. Comput 187 27-34
  • [3] Ahn H.S.(2002)Analysis of fractional delay systems of retarded and neutral type Automatica 38 1133-1138
  • [4] Chen Y.Q.(1999)Robust pole placement in LMI regions IEEE Trans. Autom. Control 44 2257-2270
  • [5] Podlubny I.(2006)Robust stability check of fractional order linear time invariant systems with interval uncertainties Signal Processing 86 2611-2618
  • [6] Bonnet C.(2003)Recent applications of fractional calculus to science and engineering Int. J. Math. Math. Sci 54 3413-3442
  • [7] Partington J.R.(1998)Some stability conditions for fractional delay systems J. of Mathematical Systems, Estimation, and Control 8 1-19
  • [8] Chilali M.(2006)A numerical algorithm for stability testing of fractional delay systems Automatica 42 825-831
  • [9] Gahinet P.(2011)Stability analysis of fractional-order systems with double noncommensurate orders for matrix case Fract. Calc. Appl. Anal 14 436-453
  • [10] Apkarian P.(2012)Impulse response of a generalized fractional second order filter Fract. Calc. Appl. Anal 15 97-116
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