Discrete-Time Matrix-Weighted Consensus

This article investigates discrete-time consensus of multiagent networks over undirected and connected graphs, whose edges are weighted by nonnegative definite matrices, under various scenarios. In particular, we first present consensus protocols for the agents in common networks of symmetric matrix weights with possibly different step sizes and switching network topologies. A special type of matrix-weighted consensus with nonsymmetric 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 convex optimization theory for Lyapunov functions with Lipschitz continuous gradients to show convergence to a consensus of the agents. Finally, simulation results are provided to illustrate the theoretical results.