This paper focuses on a new connectivity control architecture for networked multiagent systems based on hybrid protocols. Specifically, for a group of agents subject to Δ-disk proximity graphs, we consider the consensus problem while preserving connectedness with a priori given bounds on the control inputs. The bounds on the control inputs are shown not to depend on potential functions or system states. Instead the bounds are user selected continuous functions. By using the proposed framework, we show that the maximum distance among neighboring agents decreases strictly, and hence, the connectivity problem is solved while satisfying the consensus objective.