Computational and Applied Mathematics

, Volume 37, Issue 4, pp 5000–5012 | Cite as

LMI stability conditions and stabilization of fractional-order systems with poly-topic and two-norm bounded uncertainties for fractional-order α: the 1 < α < 2 case

  • Sulan Li


This article addresses the problem of robust stability and stabilization for linear fractional-order system with poly-topic and two-norm bounded uncertainties, and focuses particularly on the case of a fractional order α such that 1 < α < 2. First, the robust asymptotical stable condition is presented. Second, the design method of the state feedback controller for asymptotically stabilizing such uncertain fractional order systems is derived. In the proposed approach, linear matrix inequalities formalism is used to check and design. Lastly, two simulation examples are given to validate the proposed theoretical results.


LTI fractional-order system Poly-topic uncertainty Two-norm bounded uncertainty Stability condition Stabilization 

Mathematics Subject Classification

26A33 34H05 



The author disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This project was supported by National Natural Foundation of China (No. 51305321), National Key Basic Research Program 973 (No. 2015CB857100), the CSC Scholarship Council (No. 201606965013) and the 111 Project (No. B1402).

Author contributions

All authors contributed equally and significantly in writing this article. All authors read and approved the final manuscript

Compliance with ethical standards

Conflict of interest

The authors declared that they have no competing interest.


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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2018

Authors and Affiliations

  1. 1.Key Laboratory of Electronic Equipment Structure Design of Ministry of EducationXidian UniversityXi’anChina
  2. 2.School of Civil and Environmental EngineeringThe University of New South WalesSydneyAustralia

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