We discuss how control theoretic methods can be used to optimize the transmit power allocations in multi-user OFDMA and OFDM MIMO networks. In both cases, we focus on the downlink transmissions. We shall first examine the feasibility of the
signal-to-noise-and- interference (SINR) guarantees for downlink transmissions in relay-enhanced OFDMA networks that feature stationary users. The constraints are as follows: (i) the SINR of every user exceeds a certain threshold and (ii) the transmit power for each transmission is less than a certain threshold. We first derive a set of necessary and sufficient feasibility conditions for the specific case in which a user served by the relay station shares at most one subchannel with a user served by the base station. These conditions are a function of the target SINR values and the channel gains, and derived using a property of an M-matrix. We then extend these results to the case of networks featuring multiple base stations and multiple relays. Our conditions to check the feasibility can be easily implemented in practice. We then consider the problem of downlink transmit power allocation in multi-user MIMO wireless networks using zero-forcing beamforming. Traditionally such problems are solved by water-filling algorithm under the assumption of perfect channel knowledge. However when channel information is not known a prior or time varying the water-filling solution is shown to be unstable. We use the sliding mode control theory to synthesize the transmit powers so that the target SINR requirements of all users are met. We synthesize the sliding mode controller for the case of zero-forcing beamforming. The synthesis problem is solved assuming time-varying Rayleigh fading channel conditions. Our solutions and simulation results show that our sliding mode controller is stable and delivers better quality-of-service in real-world channel conditions.