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We develop robust power control strategies for cognitive radios in the presence of sensing delay and model parameter uncertainty. We use a discrete-time Markov chain (DTMC) to characterize the primary users' (PU) dynamics as well as the fading channel. The power control problem is formulated as a Markov decision process (MDP) problem, which can be optimally solved by dynamic programming. However, due to the time-varying nature of the wireless channel and the spectrum sensing overhead, typically only the delayed sensing results are available at any time. The delay in spectrum sensing, if not properly accounted for, could significantly deteriorate the power control performance. Furthermore, the false sensing data and limited feedback cause noisy estimate of the transition probability matrix, leading to further performance degradation of the power control and channel outage. We first propose power control schemes based on a delayed MDP formulation, that account for all possible current channel state based on the delayed channel state. In addition, we propose an outage constraint to protect PU transmissions and properly manage channel outage. We then propose a robust power control framework that optimizes the worst-case system performance. Extensive simulation results are provided to demonstrate the effectiveness of the proposed power control algorithms.