Movement consensus of complex fractional-order multi-agent systems

Due to the complexity of the practical environment, many distributed multi-agent systems can not be illustrated with the integer-order dynamics and can only be described with the fractional-order dynamics. Suppose multi-agent systems will show the individual diversity with the difference agents, where the different fractional-order dynamics are used to illustrate the agent systems and compose complex fractional compounded-order systems. Applying the Laplace transform and frequency domain theory of the fractional-order operator, the consensus of delayed multi-agent systems is studied with directed weighted topologies. Since the integer-order model is a special case of fractional-order model, the results in this paper can be extend to the compounded-order systems with integer-order models and fractional-order models. Finally, simulation examples are used to verify our results.