Distributed consensus of non-linear fractional-order multi-agent systems with directed topologies

In this study, Mittag-Leffler stability and the fractional Lyapunov direct method are used to study fractional-order leaderless and leader-following consensus algorithms with non-linear dynamics under a directed network topology. The sufficient conditions are given to guarantee that the consensus can be achieved in the non-linear fractional-order systems with and without a virtual leader, and the adaptive feedback control protocols are also given in this study. Finally, some numerical simulations are presented to demonstrate the effectiveness of the theoretical results.