Cognitive radio allows Secondary Users(SUs) to dynamically use the spectrum resource licensed to Primary Users(PUs),and significantly improves the efficiency of spectrum utilization and is viewed as a promising technology.In cognitive radio networks,the problem of power control is an important issue.In this paper,we mainly focus on the problem of power control for fading channels in cognitive radio networks.The spectrum sharing underlay scenario is considered,where SUs are allowed to coexist with PUs on the condition that the outage probability of PUs is below the maximum outage probability threshold limitation due to the interference caused by SUs.Moreover,besides the outage probability threshold which is defined to protect the performance of PUs,we also consider the maximum transmit power constraints for each SU.With such a setup,we emphasize the problem of power control to minimize the outage probability of each SU in fading channels.Then,based on the statistical information of the fading channel,the closed expression for outage probability is given in fading channels.The Dual-Iteration Power Control(DIPC) algorithm is also proposed to minimize the outage probability based on Perron-Frobenius theory and gradient descent method under the constraint condition.Finally,simulation results are illustrated to demonstrate the performance of the proposed scheme. Cognitive radio allows Secondary Users (SUs) to dynamically use the spectrum resource licensed to Primary Users (PUs), and significantly improves the efficiency of spectrum utilization and is viewed as a promising technology. In cognitive radio networks, the problem of power control is an important issue.In this paper, we mainly focus on the problem of power control for fading channels in cognitive radio networks. The spectrum sharing underlay scenario is considered, where SUs are allowed to coexist with PUs on the condition that the outage probability of PUs is below the maximum outage probability threshold limitation due to the interference caused by SUs.Moreover, besides the outage probability threshold which is defined to protect the performance of PUs, we also consider the maximum transmit power constraints for each SU .With such a setup, we emphasize the problem of power control to minimize the outage probability of each SU in fading channels. Chen, based on the statistical information of the fading channel for outage probability is given in fading channels. The Dual-Iteration Power Control (DIPC) algorithm is also proposed to minimize the outage probability based on Perron-Frobenius theory and gradient descent method under the constraint condition. simulation results are illustrated to demonstrate the performance of the proposed scheme.