Interval Bipartite Synchronization of Delayed Nonlinear Neural Networks With Signed Graphs
研究了带符号图的时滞非线性神经网络的区间二分同步问题，提出了构建Lyapunov泛函的广义矩阵，给出了耦合强度、时滞和网络结构相关的线性矩阵不等式充分条件，揭示了负根环和非负根环在稳定网络中的作用。
The cooperation of linear multiagent systems (MASs) in the signed graphs has received wide attention. However, time delays and nonlinearity are ignored. This article deals with the cooperation behavior, especially interval bipartite synchronization (IBS) of delayed nonlinear neural networks (NNs) with signed graphs. A generalized matrix is proposed for the construction of the Lyapunov functionals, establishing sufficient conditions in a linear matrix inequality related to the coupling strength, the delays, and the network structure. It suggests that the negative rooted cycles and the negative nonrooted cycles take an important part in stabilizing delayed nonlinear NNs and leading to their diversity, and time delays, especially communication delays, significantly impact cooperation performance. Numerical examples are employed to validate our derived results.