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This paper presents a simultaneous H2/H∞ optimal control problem for discrete-time systems in the state-feedback case. By the use of dynamic state feedback controllers, the design seeks to minimize the H2 norm of a closed-loop transfer matrix while simultaneously satisfying a prescribed H∞ norm bound on some other closed-loop transfer matrix. The class of problems addressed here is relatively general and consists of systems which have left invertible transfer function matrix from the control input to the controlled output. Necessary and sufficient conditions are established so that the posed simultaneous H2/H∞ problem is solvable with state feedback controllers.