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Since the complexity of the practical environment, many distributed networkedsystems can not be illustrated with the integer-order dynamics and only bedescribed as the fractional-order dynamics. Suppose multi-agent systems willshow the individual diversity with difference agents, where the heterogeneous(integer-order and fractional-order) dynamics are used to illustrate the agentsystems and compose integer-fractional compounded-order systems. ApplyingLaplace transform and frequency domain theory of the fractional-order operator,consensus of delayed multi-agent systems with directed weighted topologies isstudied. Since integer-order model is the special case of fractional-ordermodel, the results in this paper can be extend to the systems withinteger-order models. Finally, numerical examples are used to verify ourresults.

Coordination Control of Heterogeneous Compounded-Order Multi-Agent Systems with Communication Delays