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Fractional Calculus and Applied Analysis

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Volume 17, Issue 1


Robust stability bounds of uncertain fractional-order systems

YingDong Ma
  • 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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/ 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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/ WeiDong Chen
  • 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: 2013-12-28 | DOI: https://doi.org/10.2478/s13540-014-0159-3


This paper considers the robust stability bound problem of uncertain fractional-order systems. The system considered is subject either to a two-norm bounded uncertainty or to a infinity-norm bounded uncertainty. The robust stability bounds on the uncertainties are derived. The fact that these bounds are not exceeded guarantees that the asymptotical stability of the uncertain fractional-order systems is preserved when the nominal fractional-order systems are already asymptotically stable. Simulation examples are given to demonstrate the effectiveness of the proposed theoretical results.

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

Keywords: fractional-order system; linear matrix inequality; robust stability bound; uncertainty

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About the article

Published Online: 2013-12-28

Published in Print: 2014-03-01

Citation Information: Fractional Calculus and Applied Analysis, Volume 17, Issue 1, Pages 136–153, ISSN (Online) 1314-2224, DOI: https://doi.org/10.2478/s13540-014-0159-3.

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