Abstract: A novel control method for synchronization problem between two fractional order chaotic systems is proposed based on linear matrix inequality (LMI): the basic principles of fractional order math and LMI is presented; the synchronization controller based on error state function and linear feedback is designed, and the stability of the proposed controller is proved based on LMI. The proposed method retains the nonlinear dynamics of the synchronization error system, and accomplishes stable synchronization between master system and slave system via simple linear feedback control. And the parameters of this two systems are not required. Numerical simulations are performed to demonstrate the effectiveness of the proposed method.

Key words: Fractional order chaotic system, synchronization control, linear matrix inequality, linear feedback

摘要： 针对2个分数阶混沌系统的同步问题，提出一种基于线性矩阵不等式的新型控制方法：给出分数阶数学及线性矩阵不等式的基本定义；设计基于误差状态方程及线性反馈的同步控制器，并利用线性矩阵不等式理论判断所设计同步控制器的稳定性。设计的分数阶混沌系统同步控制器在保留误差系统的非线性动力学模型的基础上，利用简单的线性反馈控制实现主从系统之间的稳定同步，且不依赖于同步误差系统的具体参数。数值仿真证明了所提方法的有效性。

关键词: 分数阶混沌系统, 同步控制, 线性矩阵不等式, 线性反馈