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New results on stability and stabilization of a class of nonlinear fractional-order systems

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Abstract

The asymptotic stability and stabilization problem of a class of fractional-order nonlinear systems with Caputo derivative are discussed in this paper. By using of Mittag–Leffler function, Laplace transform, and the generalized Gronwall inequality, a new sufficient condition ensuring local asymptotic stability and stabilization of a class of fractional-order nonlinear systems with fractional-order α:1<α<2 is proposed. Then a sufficient condition for the global asymptotic stability and stabilization of such system is presented firstly. Finally, two numerical examples are provided to show the validity and feasibility of the proposed method.

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Acknowledgements

The authors thank the referees and the editor for their valuable comments and suggestions. This work was supported by the National Natural Science Funds of China for Distinguished Young Scholar under Grant (No. 50925727), the National Natural Science Foundation of China (No. 61374135), the National Defense Advanced Research Project Grant (No. C1120110004, 9140 A27020211DZ5102), the Key Grant Project of Chinese Ministry of Education under Grant (No. 313018), the Fundamental Research Funds for the Central Universities (No. 2012HGCX0003), the Natural Science Foundation of Anhui Province (No. 11040606M12), and the 211 project of Anhui University (No. KJJQ1102).

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Authors and Affiliations

  1. School of Electrical Engineering and Automation, Hefei University of Technology, Hefei, 230009, China

    Liping Chen & Yigang He

  2. School of Automation, Chongqing University, Chongqing, 400044, China

    Yi Chai

  3. School of Mathematics, Anhui University, Hefei, 230039, China

    Ranchao Wu

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  1. Liping Chen
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  2. Yigang He
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  3. Yi Chai
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  4. Ranchao Wu
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Correspondence to Liping Chen.

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Chen, L., He, Y., Chai, Y. et al. New results on stability and stabilization of a class of nonlinear fractional-order systems. Nonlinear Dyn 75, 633–641 (2014). https://doi.org/10.1007/s11071-013-1091-5

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