Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 859685, 10 pages
Research Article

Synchronization of Chaotic Fractional-Order WINDMI Systems via Linear State Error Feedback Control

1Nonlinear Dynamics and Chaos Group, School of Management, Tianjin University, Tianjin 300072, China
2Center for Applied Mathematics, School of Economics and Management, Shandong University of Science and Technology, Qingdao 266510, China
3Department of Mathematics, Dezhou University, Dezhou 253023, China

Received 25 April 2010; Accepted 20 August 2010

Academic Editor: Yuri Vladimirovich Mikhlin

Copyright © 2010 Baogui Xin 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.


We propose a fractional-order WINDMI system, as a generalization of an integer-order system developed by Sprott (2003). The considered synchronization scheme consists of identical master and slave fractional-order WINDMI systems coupled by linear state error variables. Based on the stability theory of nonlinear fractional-order systems, linear state error feedback control technique is applied to achieve chaos synchronization, and a linear control law is derived analytically to achieve synchronization of the chaotic fractional-order WINDMI system. Numerical simulations validate the main results of this work.