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Mittag–Leffler stability analysis of nonlinear fractional-order systems with impulses

Author

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  • Yang, Xujun
  • Li, Chuandong
  • Huang, Tingwen
  • Song, Qiankun

Abstract

This paper is designed to deal with the Lyapunov stability analysis of fractional-order nonlinear systems with impulses. Based on the theory of fractional calculus, impulsive differential equation and S-procedure, several sufficient criteria are established to guarantee the Mittag–Leffler stability for the addressed model with appropriate impulsive controller. Furthermore, two numerical examples are given to verify the validity and feasibility of the obtained results.

Suggested Citation

  • Yang, Xujun & Li, Chuandong & Huang, Tingwen & Song, Qiankun, 2017. "Mittag–Leffler stability analysis of nonlinear fractional-order systems with impulses," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 416-422.
    • Handle: RePEc:eee:apmaco:v:293:y:2017:i:c:p:416-422
    DOI: 10.1016/j.amc.2016.08.039
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    References listed on IDEAS

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    1. Gallegos, Javier A. & Duarte-Mermoud, Manuel A., 2016. "On the Lyapunov theory for fractional order systems," Applied Mathematics and Computation, Elsevier, vol. 287, pages 161-170.
    2. Li, Hong-Li & Jiang, Yao-Lin & Wang, Zuolei & Zhang, Long & Teng, Zhidong, 2015. "Global Mittag–Leffler stability of coupled system of fractional-order differential equations on network," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 269-277.
    3. Wu, Zeng-bao & Zou, Yun-zhi & Huang, Nan-jing, 2016. "A class of global fractional-order projective dynamical systems involving set-valued perturbations," Applied Mathematics and Computation, Elsevier, vol. 277(C), pages 23-33.
    4. Chen, Boshan & Chen, Jiejie, 2015. "Razumikhin-type stability theorems for functional fractional-order differential systems and applications," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 63-69.
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