The stability control of fractional order unified chaotic system with sliding mode control theory

doi:10.1088/1674-1056/19/10/100506

Abstract This paper studies the stability of the fractional order unified chaotic system with sliding mode control theory. The sliding manifold is constructed by the definition of fractional order derivative and integral for the fractional order unified chaotic system. By the existing proof of sliding manifold, the sliding mode controller is designed. To improve the convergence rate, the equivalent controller includes two parts: the continuous part and switching part. With Gronwall's inequality and the boundness of chaotic attractor, the finite stabilization of the fractional order unified chaotic system is proved, and the controlling parameters can be obtained. Simulation results are made to verify the effectiveness of this method.

Keywords: fractional order unified chaotic system sliding mode control stability analysis

Received: 06 February 2010
Revised: 10 March 2010
Accepted manuscript online:

PACS:	02.30.Yy	(Control theory)
	05.45.Gg	(Control of chaos, applications of chaos)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 60702023), and the Key Scientific and Technological Project of Zhejiang Province of China (Grant No. 2007C11094).

Cite this article:

Qi Dong-Lian(齐冬莲), Yang Jie(杨捷), and Zhang Jian-Liang(张建良) The stability control of fractional order unified chaotic system with sliding mode control theory 2010 Chin. Phys. B 19 100506

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