Necessary and Sufficient Conditions for Consensus of Fractional-Order Multiagent Systems via Sampled-Data Control

In this paper, the consensus of fractional-order multiagent systems (FOMASs) is considered via sampled-data control over directed communication topology with the order 0 < alpha < 1. Two cases are considered. One is FOMASs without leader, and the other is FOMASs with a leader. For each case, by applying matrix theory and algebraic graph theory, some algebraic-type necessary and sufficient conditions based on the sampling period, the fractional-order, the coupling gain, and the structure of the network are established for achieving consensus of the system. Moreover, for the network with a dynamic leader, the sampling period, the coupling gain, and the spectrum of the Laplacian matrix are carefully devised, respectively. Finally, several simulation examples are employed to validate the effectiveness of the theoretical results.