  This paper examines the cluster consensus problem of multi-agent systems on
matrix-weighted switching networks. Necessary and/or sufficient conditions
under which cluster consensus can be achieved are obtained and quantitative
characterization of the steady-state of the cluster consensus are provided as
well. Specifically, if the underlying network switches amongst finite number of
networks, a necessary condition for cluster consensus of multi-agent system on
switching matrix-weighted networks is firstly presented, it is shown that the
steady-state of the system lies in the intersection of the null space of
matrix-valued Laplacians corresponding to all switching networks. Second, if
the underlying network switches amongst infinite number of networks, the
matrix-weighted integral network is employed to provide sufficient conditions
for cluster consensus and the quantitative characterization of the
corresponding steady-state of the multi-agent system, using null space analysis
of matrix-valued Laplacian related of integral network associated with the
switching networks. In particular, conditions for the bipartite consensus under
the matrix-weighted switching networks are examined. Simulation results are
finally provided to demonstrate the theoretical analysis.
