Abstract and Applied Analysis
Volume 2012 (2012), Article ID 358201, 11 pages
http://dx.doi.org/10.1155/2012/358201
Research Article

Design of PDC Controllers by Matrix Reversibility for Synchronization of Yin and Yang Chaotic Takagi-Sugeno Fuzzy Henon Maps

Chun-Yen Ho,1 Hsien-Keng Chen,2 and Zheng-Ming Ge1

1Department of Mechanical Engineering, National Chiao Tung University, Hsinchu 300, Taiwan
2Department of Mechanical Engineering, Hsiuping University of Science and Technology, Dali City, Taichung 412, Taiwan

Received 6 June 2012; Revised 8 October 2012; Accepted 9 October 2012

Academic Editor: Zhenya Yan

Copyright © 2012 Chun-Yen Ho 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.

Abstract

This paper investigates the synchronization of Yin and Yang chaotic T-S fuzzy Henon maps via PDC controllers. Based on the Chinese philosophy, Yin is the decreasing, negative, historical, or feminine principle in nature, while Yang is the increasing, positive, contemporary, or masculine principle in nature. Yin and Yang are two fundamental opposites in Chinese philosophy. The Henon map is an invertible map; so the Henon maps with increasing and decreasing argument can be called the Yang and Yin Henon maps, respectively. Chaos synchronization of Yin and Yang T-S fuzzy Henon maps is achieved by PDC controllers. The design of PDC controllers is based on the linear invertible matrix theory. The T-S fuzzy model of Yin and Yang Henon maps and the design of PDC controllers are novel, and the simulation results show that the approach is effective.