The study investigates bipartite synchronization of inertial coupled delayed neural networks (ICDNNs) with signed digraph by non-reduced order method and pinning control. The second-order CDNNs will not be converted into a first-order differential system by introducing variable substitution. Instead, a novel Lyapunov–Krasovskii functional is proposed which depends on the topology of the ICDNNs. Some sufficient conditions for linear matrix inequalities (LMI) are derived to realize bipartite synchronization, which is based on matrix decomposition theory and Barbalat Lemma in strongly connected signed networks. And then, M-matrix theory is utilized to generalize the results to networks containing directed spanning trees. Finally, two examples are used to verify the validity of the derived theoretical results.

该研究通过无约简方法和钉扎控制研究带符号有向图的惯性耦合延迟神经网络（ICDNN）的二部同步。通过引入变量替换，将不会将二阶CDNN转换为一阶微分系统。取而代之的是，提出了一种新颖的Lyapunov–Krasovskii函数，该函数取决于ICDNN的拓扑。基于强分解的有符号网络中的矩阵分解理论和Barbalat Lemma，推导了一些足以实现线性矩阵不等式（LMI）的条件，以实现两部分同步。然后，利用M矩阵理论将结果推广到包含定向生成树的网络。最后，使用两个例子来验证所导出理论结果的有效性。