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A cognitive radio network is a multiuser system, in which different users compete for limited resources in an opportunistic manner, interacting with each other for access to the available resources. The fact that both users and spectrum holes (i.e., unused spectrum subbands) can come and go makes a cognitive radio network a highly dynamic and challenging wireless environment. Therefore, finding robust resource-allocation algorithms, which are capable of achieving reasonably good solutions fast enough in order to guarantee an acceptable level of performance under worst case interference conditions, is crucial in such environment. The focus of this paper is the transmit-power control in cognitive radio networks, considering a noncooperative framework. Moreover, tools from control theory are used to study both the equilibrium and transient behaviors of the network under dynamically varying conditions.