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This paper considers a multiple-input-multiple-output (MIMO) cognitive radio network, in which a single primary user (PU) coexists with multiple secondary users (SUs). Standard cognitive radio techniques require perfect channel state information (CSI) and are sensitive to the errors in channel estimation. In practice, such errors are inevitable due to finite feedback resources, quantization errors, and other physical constraints. As a result, robustness has become a crucial issue. Under the assumption of norm-bounded channel imperfections, we develop a robust energy-aware design that strives to admit the maximum number of served SUs and enhance the transmit rate of the secondary links while using the least transmit power while imposing the upper limit of the interference temperature to the PU. A utility function is introduced to achieve the multi-objective function by dealing with the tradeoff between maximizing the transmit rate and minimizing the transmit power. Instead of using the deterministic target, the signal-to-interference-and-noise ratio (SINR) target becomes one of the ongoing optimization variables, which is dynamically adapted with the channel condition under the pre-specified bit-error-rate (BER) requirement, and acts as admission control implicitly, i.e., the cognitive link is not allowed to transmit as long as its SINR falls to zero. Due to its nonconvexity and NP-hardness, the underlying problem is reformulated in a semidefinite programming (SDP) form and solved via an iterative bisection search approach. Simulation results are provided to validate the robustness and efficiency of the proposed scheme.