This study aims at the controllability of multi-agent systems (MASs) with cooperation and competition in a matrix-weight-based signed network based on the leader-follower structure from an algebra-theoretic perspective, which is a generalization of a scalar-weighted signed network due to increasing the dimension of controllable matrix and controllable subspace for such MASs. Therefore, comparing with existing results, relying on matrix coupling links, the study indicates that controllability can be attained in a structurally balanced matrix-weight-based network. Algebra-theoretic characterizations for attaining controllability are provided. Moreover, the algebraic uncontrollable conditions for such network are examined. Examples and simulations are given to illustrate the theoretical results.

本研究旨在从代数理论的角度研究基于领导者 - 追随者结构的基于矩阵权重的签名网络中合作和竞争的多智能体系统（MAS）的可控性，这是标量加权的推广由于增加了此类 MAS 的可控矩阵和可控子空间的维数，因此有符号网络。因此，与现有结果相比，依靠矩阵耦合链接，研究表明在结构平衡的基于矩阵权重的网络中可以获得可控性。提供了实现可控性的代数理论表征。此外，检查了这种网络的代数不可控条件。给出了例子和模拟来说明理论结果。