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| Herdability of Multi-agent Systems with Signed Matrix-weighted Networks |
| ZHU Jiahuia,b, JI Zhijiana,b, GUO Junhaoa
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| a. School of Automation; b. Academy of Systems Science and Control, Qingdao University, Qingdao 266071, China |
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Abstract 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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Published: 15 September 2026
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