This paper addresses the problem of resource allocation and precoder design in a multiuser MIMO broadcast system where the terminals are battery-powered devices provided with energy harvesting capabilities. Energy harvesting is a promising technology based on which it is possible to recharge the battery of the terminals using energy collected from the environment. Models for the power consumption of the front-end and decoding stages are discussed and included in the design of the proposed scheme. In addition, the information concerning the battery level plays an explicit role and has an impact on the design of our proposed allocation strategy. Sum-rate maximization is considered as optimization policy and energy-related constraints are taken into account explicitly in the resource allocation in order to increase the lifetime of the batteries. In the first part of the paper, we consider the transmitter to have perfect channel state information (CSI) and battery knowledge, assuming an ideal feedback link. Then, a robust design based on imperfect channel information at the transmitter is studied and its effect on the energy consumed by the terminals is analyzed. Finally, an extended robust approach considering also imperfect battery knowledge (quantized battery status) at the transmitter is also addressed. Simulation results show that our proposed technique not only improves the usage of the batteries when compared with other traditional allocation policies, but also enhances the average data rate Peer Reviewed