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Fractional Calculus and Applied Analysis

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

Jun-Guo Lu
  • Department of Automation, Shanghai Jiao Tong University and Key Laboratory of System Control and Information Processing — Ministry of Education of China, No. 800 Dong Chuan Rd., Min Hang, Shanghai, 200240, P.R. China
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/ YangQuan Chen
  • Mechatronics, Embedded Systems and Automation (MESA) Lab. School of Engineering, University of California, Merced 5200 North Lake Road, Merced, CA, 95343, USA
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Published Online: 2012-12-27 | DOI: https://doi.org/10.2478/s13540-013-0010-2


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.

MSC: Primary 26A33; Secondary 34A08, 34D10, 93C73, 93D09, 93D21

Keywords: fractional-order system; convex polytopic uncertainty; robust stability; robust stabilization; linear matrix inequality (LMI)

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About the article

Published Online: 2012-12-27

Published in Print: 2013-03-01

Citation Information: Fractional Calculus and Applied Analysis, Volume 16, Issue 1, Pages 142–157, ISSN (Online) 1314-2224, ISSN (Print) 1311-0454, DOI: https://doi.org/10.2478/s13540-013-0010-2.

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© 2013 Diogenes Co., Sofia. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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