This paper addresses the power assignment problem in multicarrier code-division multiple-access (MC-CDMA) systems. The problem is formulated as finding the correct transmission power to achieve a desired quality of service (QoS), described by an objective signal-to-interference and noise ratio (SINR). First, the model of the MC-CDMA is described, and by considering a matched filter at the receiver, the SINR after data estimation is explicitly characterized. Due to the diversity in MC-CDMA systems, the power assignment problem is approached with a minimum norm perspective restricted to achieve a pre-defined objective SINR per user. Centralized and distributed solutions are presented in the paper. The distributed power allocation strategy is further extended to consider general controllers, and measurement and processing delays. Necessary conditions for closed-loop stability and convergence to the optimal minimum norm solution are derived by using the small-gain theorem. One advantage of the proposed methodology is that it can use power control strategies previously suggested for CDMA systems, as the Foschini-Miljanic scheme and LQ-control.