Consensus on Matrix-weighted Time-varying Networks
Abstract
This paper examines the consensus problem on time-varying matrix-weighed undirected networks. First, we introduce the matrix-weighted integral network for the analysis of such networks. Under mild assumptions on the switching pattern of the time-varying network, necessary and/or sufficient conditions for which average consensus can be achieved are then provided in terms of the null space of matrix-valued Laplacian of the corresponding integral network. In particular, for periodic matrix-weighted time-varying networks, necessary and sufficient conditions for reaching average consensus is obtained from an algebraic perspective. Moreover, we show that if the integral network with period has a positive spanning tree over the time span , average consensus for the node states is achieved. Simulation results are provided to demonstrate the theoretical analysis.
Cite
@article{arxiv.2001.11179,
title = {Consensus on Matrix-weighted Time-varying Networks},
author = {Lulu Pan and Haibin Shao and Mehran Mesbahi and Yugeng Xi and Dewei Li},
journal= {arXiv preprint arXiv:2001.11179},
year = {2020}
}