Leader-following consensus of nonlinear fractional-order multi-agent systems over directed networks

This paper investigates the leader-following consensus of nonlinear fractional-order multi-agent systems where the linear part is depicted by the general linear dynamics on directed networks with the order p belonging to p(0,1] and p(1,2), respectively. By utilizing the Mittag-Leffler function, the Laplace transform, and the inequality technique, some algebraic-type consensus tracking criteria relying on the coupling strength, the coupling gain matrix and the network structure are obtained. It is interesting to find that the leader-following consensus can be attained by only using the position information among the agent and its neighbors for p(0,1] and p(1,2). The theoretical results are illustrated by several numerical simulation examples.