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In this paper, we study the problem of resource allocation and optimization for multiple-input multiple-output (MIMO) cognitive radio (CR) systems under the assumption of imperfect channel state information (CSI) of the channels between the secondary users (SUs) and the primary users (PUs) at the SUs. We formulate robust design optimization problems for CR systems with one or more SUs communicating over a single or multiple frequency carriers in the presence of multiple PUs. We propose a linear matrix inequality (LMI) transformation that facilitates proper treatment of channel uncertainty at the SU transmitter and we provide solutions to the design problems based on convex optimization and Lagrange dual decomposition techniques. Finally, we demonstrate the importance of the proposed formulations and the implications of ignoring channel uncertainties when designing for CR systems.