Fractional Calculus and Applied Analysis

, Volume 17, Issue 1, pp 136–153 | Cite as

Robust stability bounds of uncertain fractional-order systems

  • YingDong Ma
  • Jun-Guo Lu
  • WeiDong Chen
  • YangQuan Chen
Research Paper


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.

Key Words and Phrases

fractional-order system linear matrix inequality robust stability bound uncertainty 

MSC 2010

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


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Copyright information

© Versita Warsaw and Springer-Verlag Wien 2014

Authors and Affiliations

  • YingDong Ma
    • 1
  • Jun-Guo Lu
    • 1
  • WeiDong Chen
    • 1
  • YangQuan Chen
    • 2
  1. 1.Department of AutomationShanghai Jiao Tong University and Key Laboratory of System Control and Information Processing Ministry of Education of ChinaShanghaiP.R. China
  2. 2.Mechatronics, Embedded Systems and Automation (MESA) LabSchool of Engineering, University of CaliforniaMercedUSA

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