Controllability of Discrete-Time Multi-Agent Systems With Matrix-Weighted Networks

This brief studies the controllability problem of matrix-weighted discrete-time leader-follower multi-agent systems (MASs), which is a generalization of the scalar-weighted networked systems. In order to better obtain the controllable conditions of MAS, by partitioning the Laplace matrix, the controllability of MASs is transformed into the controllability of an equivalent reduced order MASs. Some conditions related to the matrix coupling network structure for the controllability of MASs are established from the perspective of algebraic theory. In addition, the influence of the relationship between leaders and followers on the controllability of MASs is discussed. Finally, a simulation is given to illustrate the theoretical results.