This article reconsiders synchronization problem of linear complex networks with time-varying delay on time scales. For different types of time scales, aperiodically intermittent control scheme is established by using a matrix-based convex combination method, which has great potential in reducing control consumption and saving communication bandwidth. By employing a common Lyapunov function, aperiodically intermittent controllers are utilized successfully to achieve synchronization of linear delayed complex networks on special time scales onto an isolated node. Next, by constructing a special Lyapunov function with time-varying coefficients, sufficient criteria that consist of two linear matrix inequalities are demonstrated to make linear delayed complex networks on general time scales synchronized onto an isolated system with an exponential convergence rate given in advance. Due to delayed complex networks in this article defined on time scales, the proposed control schemes are applicable to continuous-time networks, their discrete-time forms, and any combination of them. Four numerical examples are offered to highlight the effectiveness and superiority of the proposed aperiodically intermittent control schemes at last.

中文翻译：

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使用基于矩阵的凸组合方法通过非周期性间歇控制在时间尺度上同步延迟复杂网络

本文重新考虑了时间尺度上具有时变延迟的线性复杂网络的同步问题。针对不同类型的时间尺度，采用基于矩阵的凸组合方法建立非周期性间歇控制方案，在降低控制消耗和节省通信带宽方面具有巨大潜力。通过采用共同的 Lyapunov 函数，非周期性间歇控制器被成功地用于实现特殊时间尺度上的线性延迟复杂网络与孤立节点的同步。接下来，通过构造一个特殊的具有时变系数的李雅普诺夫函数，证明了由两个线性矩阵不等式组成的充分标准可以使一般时间尺度上的线性延迟复杂网络同步到具有预先给定的指数收敛率的孤立系统上。由于本文中在时间尺度上定义的延迟复杂网络，所提出的控制方案适用于连续时间网络、它们的离散时间形式以及它们的任意组合。最后提供了四个数值例子来强调所提出的非周期性间歇控制方案的有效性和优越性。