## Abstract and Applied Analysis

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

#### Abstract

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 $t$ tends to infinity. Finally, the numerical simulations are also presented.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 620286, 10 pages.

Dates
First available in Project Euclid: 26 February 2014

https://projecteuclid.org/euclid.aaa/1393447695

Digital Object Identifier
doi:10.1155/2013/620286

Mathematical Reviews number (MathSciNet)
MR3049413

Zentralblatt MATH identifier
1271.93114

#### Citation

Zhou, Guopeng; Huang, Jinhua; Liao, Xiaoxin; Cheng, Shijie. Stability Analysis and Control of a New Smooth Chua's System. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 620286, 10 pages. doi:10.1155/2013/620286. https://projecteuclid.org/euclid.aaa/1393447695

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