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The problem considered in the paper is the design of a feedback control law such that the closed loop system meets desired performance specifications. Particularly, the authors are dealing with the exact model matching problem for systems with two dimensions, using periodic state and output feedback, assuming that the states and the output are accessible to measurements, and that noise is not present. The method leads to necessary conditions for the solution of the problem. To illustrate the procedure, two step-by-step examples are presented.