In this paper, we contribute to the further development of delay-range-dependent state-feedback aspect of robust control for vibration reduction in a building structure with limited wireless communication capacity subjected to measurement quantization, signal transmission delay and data packet dropout, which appear typically in a network environment. The feedback loop is subjected to a time-varying bounded delay within the sensors and the structure. By using an appropriate Lyapunov-Krasovskii functional and some free weighting matrices, new sufficient conditions in terms of some linear matrix inequalities are established for the existence of desired controllers such that the resulting closed-loop system is asymptotically stable and kept within a prescribed level of H1 performance bound. Finally, simulation results are given to illustrate the usefulness of the proposed control methodology.