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

doi:10.1088/1674-1056/20/9/090508

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)

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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
[2]	Podlubny I 1999 Fractional Differential Equations (New York: Academic Press) p. 71
[3]	Kreyszig E 1978 Introductory Functional Analysis with Applications (Somerset: John Wiley & Sons) p. 59
[4]	Li Y, Chen Y Q and Podlubny I 2009 Automatica 45 1965
[5]	Efe M O 2008 IEEE Trans. Syst. Man Cybern. B 38 1561

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