Adaptive Consensus of Matrix Weighted Network

In this study, the adaptive consensus of linear multiagent systems with a matrix-weighted network is investigated. The proposed protocol employs a simple adaptation law to adjust its coupling weight in a monotonically increasing manner and uses only local information received from neighboring agents. Moreover, it is shown that the proposed method can solve the consensus problem for matrix-weighted networks, and its adaptive gain is bounded and converges to a constant value. Finally, the validity of the proposed scheme is demonstrated using a numerical example of a matrix-weighted network.