Abstract
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.
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