中国物理B ›› 2011, Vol. 20 ›› Issue (9): 90508-090508.doi: 10.1088/1674-1056/20/9/090508

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Comments on “The feedback control of fractional order unified chaotic system”

Elham Amini Boroujeni, Hamid Reza Momeni   

  1. Automation and Instruments Laboratory, Electrical Engineering Department, Tarbiat Modares University, Tehran, Iran
  • 收稿日期:2011-01-23 修回日期:2011-04-09 出版日期:2011-09-15 发布日期:2011-09-15

Comments on “The feedback control of fractional order unified chaotic system”

Elham Amini Boroujeni and Hamid Reza Momeni†   

  1. Automation and Instruments Laboratory, Electrical Engineering Department, Tarbiat Modares University, Tehran, Iran
  • Received:2011-01-23 Revised:2011-04-09 Online:2011-09-15 Published:2011-09-15

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摘要： Our comments point out some mistakes in the main theorem given by Yang and Qi in Ref. [1] concerning the equivalent passivity method to design a nonlinear controller for the stabilizing fractional order unified chaotic system. The proof of this theorem is not reliable, since the mathematical basis of the fractional order calculus is not considered. Moreover, there are some algebraic mistakes in the inequalities used, thus making the proof invalid. We propose a proper Lyapunov function and the stability of Yang and Qi's Controller is investigated based on the fractional order Lyapunov theorem.

Abstract: Our comments point out some mistakes in the main theorem given by Yang and Qi in Ref. [1] concerning the equivalent passivity method to design a nonlinear controller for the stabilizing fractional order unified chaotic system. The proof of this theorem is not reliable, since the mathematical basis of the fractional order calculus is not considered. Moreover, there are some algebraic mistakes in the inequalities used, thus making the proof invalid. We propose a proper Lyapunov function and the stability of Yang and Qi's Controller is investigated based on the fractional order Lyapunov theorem.

Key words: fractional order calculus, Lyapunov function

中图分类号:  (Control of chaos, applications of chaos)

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