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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 128580, 14 pages
Research Article

Linear Matrix Inequality Based Fuzzy Synchronization for Fractional Order Chaos

Department of Electrical Engineering, Northwest A&F University, Yangling 712100, China

Received 8 December 2014; Accepted 27 March 2015

Academic Editor: Evangelos J. Sapountzakis

Copyright © 2015 Bin Wang 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 investigates fuzzy synchronization for fractional order chaos via linear matrix inequality. Based on generalized Takagi-Sugeno fuzzy model, one efficient stability condition for fractional order chaos synchronization or antisynchronization is given. The fractional order stability condition is transformed into a set of linear matrix inequalities and the rigorous proof details are presented. Furthermore, through fractional order linear time-invariant (LTI) interval theory, the approach is developed for fractional order chaos synchronization regardless of the system with uncertain parameters. Three typical examples, including synchronization between an integer order three-dimensional (3D) chaos and a fractional order 3D chaos, anti-synchronization of two fractional order hyperchaos, and the synchronization between an integer order 3D chaos and a fractional order 4D chaos, are employed to verify the theoretical results.