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
- 55 Downloads
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.
KeywordsLTI fractional-order system Poly-topic uncertainty Two-norm bounded uncertainty Stability condition Stabilization
Mathematics Subject Classification26A33 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).
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.
- Sabermahani S, Ordokhani Y, Yousefi SA (2017) Numerical approach based on fractional-order Lagrange polynomials for solving a class of fractional differential equations. Comput Appl Math 1–23. https://doi.org/10.1007/s40314-017-0547-5
- Xue D, Zhao C, Chen Y (2006) Fractional order PID controller of a DC-motor with elastic shaft: a case study. In: Proceedings of the 2006 American control conference, Minneapolis, Minnesota, USA, June 14–16. https://doi.org/10.1109/ACC.2006.1657207