Discrete-Time Matrix-Weighted Consensus

TL;DR

This paper explores discrete-time consensus protocols for multi-agent systems using matrix weights, including symmetric and non-symmetric cases, with stability analysis and simulations demonstrating convergence.

Contribution

It introduces new consensus protocols with matrix weights, including non-symmetric types, and provides stability analysis for convergence in discrete-time multi-agent networks.

Findings

Consensus is achieved under symmetric matrix weights with different update rates.

Non-symmetric matrix weights enable scaled, rotated, or affine consensus scenarios.

Simulation results confirm theoretical convergence properties.

Abstract

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.