Consensus of fractional-order multi-agent systems with sampled position data

In this paper, the consensus of fractional-order multi-agent systems with the order alpha satisfying alpha is an element of (0, 1] is investigated. A novel distributed control protocol is constructed, in which only the past sampled position data of neighbors are utilized. Then, based on Laplace transform, Mittag-Leffler function, and matrix theory, necessary and sufficient criteria depending on the order, coupling gains, sampling period, and communication topology, are established to attain consensus for the systems. Meanwhile, the intervals of coupling gains and sampling period associated with the maximum eigenvalue of Laplacian matrix over an undirected graph are presented to attain consensus. Finally, the availability of theoretical results is verified by numerical simulations. (c) 2023 The Franklin Institute. Published by Elsevier Inc. All rights reserved.