In this work the connectivity preserving problem of multiple agents with limited communication ranges in the context of rendezvous tasks has been investigated. The communication among agents is considered to be unreliable and the control inputs of agents are required to be bounded. Based on the explicitly defined virtual neighbors, the proximity graph connectivity of the agent group has been preserved. Moreover, by using the constraint function approach, the control inputs are guaranteed to be bounded, which can be easily implemented in practice. It is proved that the proposed control law can not only ensure union connectivity of the underlying communication graph, but also drive the agents to rendezvous. The effectiveness of the control law is illustrated by numerical examples. (C) 2013 Elsevier Ltd. All rights reserved.