The present work concerns the multi-group consensus behavior of directed complex networks. The network consists of agents with heterogeneous fractional-order non-linear dynamics. It can be divided into several groups due to their dynamics or equilibriums. Each group will be stabilized at an equilibrium and different groups may have different steady state values. A necessary and sufficient condition is provided for the proposed pinning control law to be locally Mittag-Leffler stable. The conclusion turns to guarantee the exponential stable for integer-order systems. The collection of heterogeneous equilibriums is determined by the geometric multiplicity of the zero eigenvalue respect to the graph Laplacian. Simulations on fractional-order chaotic systems demonstrated the conclusions.

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