Abstract This paper considers the synchronization problem of nonlinear complex dynamical networks (CDNs) through intermittent pinning control approach on time scales. Both the internal delay and coupling delay are considered in the nonlinear CDNs. To deal with the nonlinearity in the delayed complex network, a new scale-limited differential inequality is proposed. Based on the Lyapunov approach and the theory of time scales, some novel exponential synchronization criteria are derived, which are applicable not only to the continuous/discrete CDNs but also to the case of continuous–discrete hybrid time domains. Two numerical examples are provided to certify the validness of the proposed design method.

中文翻译：

---

通过时间尺度上的间歇钉扎控制非线性复杂网络的指数同步

摘要 本文通过时间尺度上的间歇钉扎控制方法考虑非线性复杂动态网络（CDN）的同步问题。非线性 CDN 中同时考虑了内部延迟和耦合延迟。针对延迟复杂网络中的非线性问题，提出了一种新的尺度有限微分不等式。基于李雅普诺夫方法和时间尺度理论，推导出了一些新的指数同步标准，它们不仅适用于连续/离散 CDN，也适用于连续-离散混合时域的情况。提供了两个数值例子来证明所提出的设计方法的有效性。