Xu Yao, Liu Jingjing, Li Wenxue
Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai 264209, PR China.
Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai 264209, PR China.
Neural Netw. 2022 Jun;150:43-57. doi: 10.1016/j.neunet.2022.02.023. Epub 2022 Mar 4.
The paper is devoted to investigating the quasi-synchronization issue of fractional-order multi-layer networks with mismatched parameters under delay-dependent impulsive feedback control. It is worth highlighting that fractional-order multi-layer networks with mismatched parameters, as the extension model for single-layer or two-layer ones, are constructed in this paper. Simultaneously, the intra-layer and inter-layer couplings are taken into consideration, which is more general and rarely considered in discussions of network synchronization. An extended fractional differential inequality with impulsive effects is given to establish the grounded framework and theory on the quasi-synchronization problem under delay-dependent impulsive feedback control. Moreover, in the light of the Lyapunov method and graph theory, two criteria for achieving the quasi-synchronization of fractional-order multi-layer networks with mismatched parameters are derived. Furthermore, exponential convergence rates as well as the bounds of quasi-synchronization errors are successfully deduced. Ultimately, the theoretical results are applied in a practical power system, and some illustrative examples are proposed to show the effectiveness of theoretical analysis.
本文致力于研究在依赖延迟的脉冲反馈控制下参数不匹配的分数阶多层网络的准同步问题。值得强调的是，本文构建了参数不匹配的分数阶多层网络，作为单层或两层网络的扩展模型。同时，考虑了层内和层间耦合，这在网络同步讨论中更为普遍且很少被考虑。给出了一个具有脉冲效应的扩展分数阶微分不等式，以建立依赖延迟的脉冲反馈控制下准同步问题的基础框架和理论。此外，根据李雅普诺夫方法和图论，推导了实现参数不匹配的分数阶多层网络准同步的两个准则。进一步成功推导了指数收敛速率以及准同步误差的界。最终，将理论结果应用于一个实际电力系统，并给出了一些示例以说明理论分析的有效性。
