Abstract
Abstract This study concentrates on achieving quasi‐bipartite synchronization within signed coupled inertial neural networks featuring time‐varying delays. The pinning controller technique addresses this problem within a structure incorporating cooperative and competitive interaction among the nodes. With the structurally balanced networks, some linear matrix inequality based sufficient conditions are derived for both reduced and non‐reduced order methods with the help of Lyapunov–Krasovskii functional to achieve the quasi‐bipartite pinning synchronization criterion. Further, the error bound is derived analytically for the leader–follower representation of the signed coupled inertial neural network model. At last, a numerical simulation result is provided to verify the correctness of the established theoretical results.