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Stabilization of the unstable equilibrium points of the fractional-order BLDCM chaotic system in the sense of Lyapunov by a single-state variable

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Abstract

Based on the fractional-order extension of the Lyapunov direct method, this paper proposes a control scheme determined by a single-state variable, and the unstable equilibrium points of the fractional-order brushless DC motors are stabilized in the sense of Lyapunov. By means of Lyapunov candidate function, the proof of stability in the sense of Lyapunov is given. Simulation results show that the control scheme in this paper is valid.

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Authors and Affiliations

  1. Center of System Theory and Its Applications, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China

    Ping Zhou & Chunde Yang

  2. Key Laboratory of Network Control and Intelligent Instrument of Ministry of Education, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China

    Hao Cai

Authors
  1. Ping Zhou
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  2. Hao Cai
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  3. Chunde Yang
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Correspondence to Ping Zhou or Chunde Yang.

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Zhou, P., Cai, H. & Yang, C. Stabilization of the unstable equilibrium points of the fractional-order BLDCM chaotic system in the sense of Lyapunov by a single-state variable. Nonlinear Dyn 84, 2357–2361 (2016). https://doi.org/10.1007/s11071-016-2649-9

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  • DOI: https://doi.org/10.1007/s11071-016-2649-9

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