研究了符号有向图下,一般线性和矩阵权重多智能体系统的可聚集性问题。首先,利用能控性结构分解给出了一般线性多智能体系统可聚集的充分条件。其次,结合能控子空间和图论,提出了一类矩阵权重下多智能体系统可聚集的图论条件。最后,提出符号矩阵权重距离等价划分的定义,给出了在该划分下的一般矩阵权重可聚集的判定条件,发现权重矩阵的非零元素同为正值或同为负值时系统可聚集。
This paper investigates the herdability of multi-agent systems with general linear and signed matrix-weighted networks under signed directed graphs. Firstly, we present the sufficient conditions for herdability of general linear multi-agent systems by utilizing controllability structure decomposition. Moreover, leveraging the concepts of controllable subspaces and graph theory, we propose a set of graph-theoretic conditions for the herdability of multi-agent systems under different matrix weight scenarios. Finally, we introduce the definition of signed matrix-weighted distance-equivalent partitioning and provide the herdability criteria for general matrix-weighted networks under this partitioning. It is found that the system is herdable when the non-zero elements of the weight matrix are either all positive or all negative.
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