奇异分数阶复杂动态网络的鲁棒同步:LMI法

Linear Matrix Inequality Criteria for Robust Synchronization of Singular Fractional-Order Complex Dynamical Networks

为解决奇异分数阶复杂动态网络的同步问题,将连续频率分布等价模型引入到分数阶奇异系统中,应用间接李雅普诺夫方法,通过设计同步控制器将奇异系统正常化,给出阶次在0<α<1范围内能使不确定奇异分数阶复杂动态网络同步全新的充分条件。利用Matlab的LMI(Linear Matrix Inequalities)工具箱求解控制器的增益。通过仿真算例及数据验证,表明该方法可有效地解决复杂动态网络同步问题。

In order to solve the problem of the synchronization for singular fractional-order complex dynamic networks,the continuous frequency distributed equivalent model and the indirect Lyapunov approach are applied in the research of the singular fractional-order systems,a fractional-order synchronization controller is proposed to normalize the singular fractional-order system.A novel sufficient condition for synchronization of uncertain singular fractional-order complex dynamic networks with the order α（0α1） is presented.The LMI（Linear Matrix Inequalities） techniques is used to obtain the gain of controller.A numerical example is provided to demonstrate the validity of the proposed methods.