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在整数阶混沌系统投影同步的基础上,提出了分数阶混沌系统的全状态混合投影同步.基于分数阶线性系统稳定性理论和矩阵理论,结合非线性反馈控制与主动控制方法提出分数阶混沌系统的全状态混合投影同步控制器设计方法,理论上证明了该设计方法的可行性.同时以一个新分数阶超混沌系统为例,运用数值仿真验证所设计控制器的有效性.最后采用混沌遮掩方法,将全状态混合投影同步应用在保密通信中.仿真结果表明,两个分数阶混沌系统可以实现快速同步且可以无失真地恢复有用信号.
Based on the projective synchronization of integer order chaotic system, the hybrid state projection of fractional order chaotic system is proposed. Based on the theory of fractional order linear system stability and matrix theory, combined with the nonlinear feedback control and active control method, the fractional order chaotic system , A new fractional-order hyperchaotic system is taken as an example to verify the effectiveness of the proposed controller.Finally, the chaos masking Method, the hybrid state-of-the-art projection is applied in secure communication.The simulation results show that the two fractional-order chaotic systems can achieve fast synchronization and recover useful signals without distortion.