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This paper investigates the cluster consensus control for generic linear multi-agent systems (MASs) under directed interaction topology via distributed feedback controller. Focus of this paper is particularly on addressing the following problem which is of both theoretical and practical interests but have not been considered in the existing literature: under what kind of interaction among the clusters can the cluster consensus control be achieved regardless of the magnitude of the coupling strengths among the agents? Directed acyclic interaction topology among the clusters is proved to have this property. Our results are proved to be applicable to tackle similar problem arising in cluster consensus of integrator agents, in which to reach the cluster consensus the interaction topology of each cluster is only required to have a spanning tree. Conditions for guaranteeing the cluster consensus control are presented in terms of purely the structure of the interaction topology and thus are very easy to be verified.