  This article investigates discrete-time matrix-weighted consensus of
multi-agent networks over undirected and connected graphs. We first present
consensus protocols for the agents in common networks of symmetric matrix
weights with possibly different update rates and switching network topologies.
A special type of matrix-weighted consensus with non-symmetric matrix-weights
that can render several consensus control scenarios such as ones with
scaled/rotated updates and affine motion constraints is also considered. We
employ Lyapunov stability theory for discrete-time systems and occasionally
utilize Lipschitz continuity of the gradient of the Lyapunov function to show
the convergence to a consensus of the agents in the system. Finally, simulation
results are provided to illustrate the theoretical results.
