Mathematical Problems in Engineering
Volume 2007 (2007), Article ID 86852, 10 pages
Research Article

Chaos Synchronization Criteria and Costs of Sinusoidally Coupled Horizontal Platform Systems

Jianping Cai,1 Xiaofeng Wu,2 and Shuhui Chen1

1Department of Applied Mechanics and Engineering, Zhongshan University, Guangzhou 510275, China
2Center for Control and Optimization, South China University of Technology, Guangzhou 510640, China

Received 24 September 2006; Revised 12 December 2006; Accepted 11 February 2007

Academic Editor: José Manoel Balthazar

Copyright © 2007 Jianping Cai 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.


Some algebraic sufficient criteria for synchronizing two horizontal platform systems coupled by sinusoidal state error feedback control are derived by the Lyapunov stability theorem for linear time-varying system and Sylvester's criterion. The state variables are restricted in a subregion in order to obtain easily verified criteria. The validity of these algebraic criteria is illustrated with some numerical examples. A new concept, synchronization cost, is introduced based on a measure of the magnitude of the feedback control. The minimal synchronization cost as well as optimal coupling strength is calculated numerically. The results are meaningful in engineering application.