Linear Matrix Inequality Based Fuzzy Synchronization for Fractional Order Chaos. (15th July 2015)

• Record Type: Journal Article
• Authors: Wang, Bin; Cao, Hongbo; Wang, Yuzhu; Zhu, Delan
• Other Names: Sapountzakis Evangelos J. Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2015(2015)
• Publication Date: 2015-07-15
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2015/128580
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : 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.