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Abstract and Applied Analysis
Volume 2013, Article ID 620286, 10 pages
Research Article

Stability Analysis and Control of a New Smooth Chua's System

1College of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
2College of Electronic and Information Engineering, Hubei University of Science and Technology, Xianning 437100, China
3Department of Electric and Electronic Engineering, Wuhan Institute of Shipbuilding Technology, Wuhan 430050, China
4Department of Control and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China

Received 3 December 2012; Accepted 7 April 2013

Academic Editor: René Yamapi

Copyright © 2013 Guopeng Zhou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper is concerned with the stability analysis and control of a new smooth Chua's system. Firstly, the chaotic characteristic of the system is confirmed with the aid of the Lyapunov exponents. Secondly, it is proved that the system has globally exponential attractive set and positive invariant set. For the three unstable equilibrium points of the system, a linear controller is designed to globally exponentially stabilize the equilibrium points. Then, a linear controller and an adaptive controller are, respectively, proposed so that two similar types of smooth Chua's systems are globally synchronized, and the estimation errors of the uncertain parameters converge to zero as tends to infinity. Finally, the numerical simulations are also presented.