Based on some essential concepts of fractional calculus and the theorem related to the fractional extension of Lyapunov direct method, we present in this paper a synchronization scheme of fractional-order Lur’e systems. A quadratic Lyapunov function is chosen to derive the synchronization criterion. The derived criterion is a suffcient condition for the asymptotic stability of the error system, formulated in the form of linear matrix inequality (LMI). The controller gain can be achieved by solving the LMI. The proposed scheme is illustrated for fractional-order Chua’s circuits and fractional-order four-cell CNN. Numerical results, which agree well with the proposed theorem, are given to show the effectiveness of this scheme.

中文翻译：

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分数阶Lur'e系统的混沌同步

基于分数阶微积分的一些基本概念和与Lyapunov直接法分数扩展有关的定理，本文提出了分数阶Lur'e系统的同步方案。选择二次 Lyapunov 函数来导出同步标准。导出的准则是误差系统渐近稳定性的充分条件，以线性矩阵不等式 (LMI) 的形式表示。控制器增益可以通过求解LMI来实现。所提出的方案针对分数阶 Chua 电路和分数阶四单元 CNN 进行了说明。数值结果与所提出的定理很好地吻合，证明了该方案的有效性。