## Journal of Applied Mathematics

• J. Appl. Math.
• Volume 2013, Special Issue (2013), Article ID 856282, 10 pages.

### Adaptive Sliding Mode Controller Design for Projective Synchronization of Different Chaotic Systems with Uncertain Terms and External Bounded Disturbances

#### Abstract

Synchronization is very useful in many science and engineering areas. In practical application, it is general that there are unknown parameters, uncertain terms, and bounded external disturbances in the response system. In this paper, an adaptive sliding mode controller is proposed to realize the projective synchronization of two different dynamical systems with fully unknown parameters, uncertain terms, and bounded external disturbances. Based on the Lyapunov stability theory, it is proven that the proposed control scheme can make two different systems (driving system and response system) be globally asymptotically synchronized. The adaptive global projective synchronization of the Lorenz system and the Lü system is taken as an illustrative example to show the effectiveness of this proposed control method.

#### Article information

Source
J. Appl. Math., Volume 2013, Special Issue (2013), Article ID 856282, 10 pages.

Dates
First available in Project Euclid: 7 May 2014

https://projecteuclid.org/euclid.jam/1399493302

Digital Object Identifier
doi:10.1155/2013/856282

Mathematical Reviews number (MathSciNet)
MR3082122

Zentralblatt MATH identifier
1271.34056

#### Citation

Cang, Shijian; Wang, Zenghui; Chen, Zengqiang. Adaptive Sliding Mode Controller Design for Projective Synchronization of Different Chaotic Systems with Uncertain Terms and External Bounded Disturbances. J. Appl. Math. 2013, Special Issue (2013), Article ID 856282, 10 pages. doi:10.1155/2013/856282. https://projecteuclid.org/euclid.jam/1399493302

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