具有时变时滞的不连续复杂网络固定与预定时间同步
Fixed/Preassigned-Time Synchronization of Discontinuous Complex Networks with Time-Varying Delays
摘要: 本文研究了同时具有内部时变时滞和耦合时变时滞的不连续复杂网络的固定时间与预定时间同步问题。基于固定时间稳定性定理及其引理，设计了新的状态反馈控制器，实现了复杂网络的固定与预定时间同步。在Filippov微分包含框架下，通过应用Lyapunov-Krasovskii泛函方法和不等式分析方法，以线性矩阵不等式的形式得到了含有时滞的不连续复杂网络的固定时间与预定时间同步判定准则。最后用数值模拟验证了控制器的有效性与理论的正确性。
Abstract: In this paper, we study the fixed-time and pre-assigned-time synchronization of discontinuous com-plex networks with both internal time-varying delays and coupled time-varying delays. Based on the fixed-time stability theorem and its lemma, a new state feedback controller is designed to real-ize the fixed and pre-assigned time synchronization of complex networks. Under the framework of Filippov differential inclusion, by using Lyapunov-Krasovskii functional method and inequality analysis method, the criterion of fixed time and pre-assigned time synchronization for discontinu-ous complex networks with time delay is obtained in the form of linear matrix inequalities. Finally, the effectiveness of the controller and the correctness of the theory are verified by numerical simu-lation.
文章引用：李兴瑞, 单美华, 史东鑫. 具有时变时滞的不连续复杂网络固定与预定时间同步[J]. 应用数学进展, 2022, 11(9): 6799-6810. https://doi.org/10.12677/AAM.2022.119720

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