Error Estimation for Quasi-Synchronization of Multilayer Dynamical Networks: A Pinning Delayed Impulsive Control Scheme
研究了一类多层动态网络的准同步误差估计问题，设计了利用大规模脉冲延迟和牵制节点数的脉冲控制策略，推导出收敛域和误差界的解析表达式，并通过多层单连杆机器人臂网络验证了有效性。
In this article, we address the error estimation problem of quasi-synchronization for a class of multilayer dynamical networks. The proposed network model simultaneously accounts for interlayer and intralayer time-varying coupling structures, network directionality, and interlayer communication delays. To achieve synchronization in a cost-effective manner, we design a novel pinning impulsive control strategy that leverages large-scale impulse delay information together with the number of pinned nodes. By employing an iterative algorithm, we establish a new delay-dependent impulsive differential inequality, which precisely characterizes the convergence domain and provides flexibility in the choice of impulse delays. Then, some quasi-synchronization criteria are derived to guarantee convergence of multilayer networks within a prescribed error level, and explicit analytical expressions for the synchronization error bounds are obtained. Finally, to demonstrate the practical applicability, the proposed criteria are applied to the synchronization of multilayer single-link robot arm networks under error bounds, with numerical examples validating the effectiveness of the method.