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Chin. Phys. B, 2010, Vol. 19(2): 020508    DOI: 10.1088/1674-1056/19/2/020508
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The feedback control of fractional order unified chaotic system

Yang Jie(杨捷) and Qi Dong-Lian(齐冬莲)
College of Electrical Engineering, Zhejiang University, Hangzhou 310027, China
Abstract  This paper studies the stability of the fractional order unified chaotic system. On the unstable equilibrium points, the ``equivalent passivity'' method is used to design the nonlinear controller. With the definition of fractional derivatives and integrals, the Lyapunov function is constructed by which it is proved that the controlled fractional order system is stable. With Laplace transform theory, the equivalent integer order state equation from the fractional order nonlinear system is obtained, and the system output can be solved. The simulation results validate the effectiveness of the theory.
Keywords:  state feedback control      fractional order      unified chaotic system      Lyapunov function  
Received:  03 April 2009      Revised:  11 June 2009      Accepted manuscript online: 
PACS:  05.45.Gg (Control of chaos, applications of chaos)  
  02.30.Yy (Control theory)  
  02.30.Uu (Integral transforms)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No.~60702023) and Natural Science Foundation of Zhejiang Province (Grant No.~Y107440).

Cite this article: 

Yang Jie(杨捷) and Qi Dong-Lian(齐冬莲) The feedback control of fractional order unified chaotic system 2010 Chin. Phys. B 19 020508

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