Cluster consensus in multi-partitioned matrix weighted graphs

A set of agents interacting with each other using matrix-weighted graphs to achieve multiple clusters has been discussed in detail in this paper. The conditions for achieving the multi-cluster formation have been derived. It is shown that a certain type of clustering of agent states will be achieved exponentially fast for almost all initial conditions if the matrix weighted graph is multi-partitioned and structurally balanced. The results are supported with numerical simulation.