Both cognitive radio (CR) and full duplex transmissions are effective means to enhance spectrum efficiency and network capacity. In this paper, we investigate the problem of power control in an underlay CR network where the CR nodes are capable of full-duplex (FD) transmissions. The objective is to guarantee the required quality of service (QoS) in the form of a minimum signal-to-interference-plus-noise (SINR) ratio at each CR user and keep the interference to primary users below a prescribed threshold. We design an effective distributed power control scheme that integrates a proportional-integral-derivative (PID) controller and a power constraint mechanism to achieve the above goals. We analyze the stability performance of the proposed scheme and develop a hybrid scheme that can switch between FD and half duplex (HD) modes. The proposed scheme is validated with extensive simulations. (C) 2015 Elsevier B.V. All rights reserved.