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Linear Matrix Inequality Based Fuzzy Synchronization for Fractional Order Chaos

Author

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  • Bin Wang
  • Hongbo Cao
  • Yuzhu Wang
  • Delan Zhu

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.

Suggested Citation

  • Bin Wang & Hongbo Cao & Yuzhu Wang & Delan Zhu, 2015. "Linear Matrix Inequality Based Fuzzy Synchronization for Fractional Order Chaos," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-14, July.
    • Handle: RePEc:hin:jnlmpe:128580
    DOI: 10.1155/2015/128580
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