Distributed coordination of fractional order multi-agent systems with communication delays

Because of the complexity of the practical environments, many distributed multi-agent systems can not be illustrated with the integer-order dynamics and can only be described with the fractional-order dynamics. Under the connected network with directed weighted topologies, the dynamical characteristics of agents with fractional-order derivative operator is analyzed in this paper. Applying the Laplace transform and frequency domain theory of the fractional-order operator, the distributed coordination of fractional-order multi-agent systems (FOMAS) with communication delays is studied, and a critical value of time delay is obtained to ensure the consensus of FOMAS. Since the integer-order model is a special case of fractional-order model, the extended results in this paper are in accordance with that of the integer-order model. Finally, numerical examples are provided to verify our results.