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The important transfer function design problems of input-output decoupling, exact model matching and disturbance rejection, via static measurement output feedback, are studied for the case of generalized state space systems. Necessary and sufficient conditions for the solvability of these problems are established. The general analytical expressions of the respective controller matrices are derived. The above results are also extended to cover the combined problem of disturbance rejection with simultaneous decoupling and the problem of disturbance rejection with simultaneous exact model matching.