This paper examines the stability and distributed stabilization of signed multi-agent networks. Here, positive semidefiniteness is not inherent for signed Laplacians, which renders the stability and consensus of this category of networks intricate. First, we examine the stability of signed networks by introducing a novel graph-theoretic objective negative cut set, which implies that manipulating negative edge weights cannot change a unstable network into a stable one. Then, inspired by the diagonal dominance and stability of matrices, a local state damping mechanism is introduced using self-loop compensation. The self-loop compensation is only active for those agents who are incident to negative edges and can stabilize signed networks in a fully distributed manner. Quantitative connections between self-loop compensation and the stability of the compensated signed network are established for a tradeoff between compensation efforts and network stability. Necessary and/or sufficient conditions for predictable cluster consensus of compensated signed networks are provided. The optimality of self-loop compensation is discussed. Furthermore, we extend our results to directed signed networks where the symmetry of signed Laplacian is not free. The correlation between the stability of the compensated dynamics obtained by self-loop compensation and eventually positivity is further discussed. Novel insights into the stability of multi-agent systems on signed networks in terms of self-loop compensation are offered. Simulation examples are provided to demonstrate the theoretical results.

翻译：本文审视了签名的多试剂网络的稳定性和分布式稳定性。 这里, 积极的半限值对于签名的 Laplacian 来说并非固有, 这使得这一类网络的稳定性和共识变得错综复杂。 首先, 我们通过引入新型的图形理论目标负切分来审视签名网络的稳定性。 这意味着操纵负边权重不能将不稳定的网络改变为稳定的网络。 然后, 在对角支配地位和矩阵稳定性的启发下, 采用自我覆盖补偿机制 。 自我覆盖补偿机制只对那些出现负面边缘事件并能以完全分布的方式稳定签名网络的人有效。 自我loop补偿与补偿签名网络稳定之间的定量连接, 补偿努力与网络稳定之间的平衡性联系; 提供必要和/ 或充分条件,使补偿网络的可预见性集群共识变成稳定。 自我覆盖补偿的最佳性讨论。 此外, 我们将结果推广给已经签名的Laplaceian 的对称对称不自由的网络。 已经签署的理论性网络的稳定性与通过自我定位系统获得的自我定位, 最终在自我定位上得到的模拟补偿。