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Chin. Phys. B, 2011, Vol. 20(9): 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 and Hamid Reza Momeni
Automation and Instruments Laboratory, Electrical Engineering Department, Tarbiat Modares University, Tehran, Iran
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.
Keywords:  fractional order calculus      Lyapunov function  
Received:  23 January 2011      Revised:  09 April 2011      Accepted manuscript online: 
PACS:  05.45.Gg (Control of chaos, applications of chaos)  

Cite this article: 

Elham Amini Boroujeni and Hamid Reza Momeni Comments on “The feedback control of fractional order unified chaotic system” 2011 Chin. Phys. B 20 090508

[1] Yang J and Qi D L 2010 Chin. Phys. B 19 020508
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