Consensus of compound-order multi-agent systems with communication delays

In complex environments, many distributed networked systems can only be illustrated with fractional-order dynamics. When multi-agent systems show individual diversity with difference agents, heterogeneous (integer-order and fractional-order) dynamics are used to illustrate the agent systems and compose integerfractional compounded-order systems. Applying Laplace transform and frequency domain theory of the fractional-order operator, the consensus of delayed multi-agent systems with directed weighted topologies is studied. Since an integer-order model is the special case of a fractional-order model, the results in this paper can be extended to systems with integer-order models. Finally, numerical examples are used to verify our results.