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In this paper "Generalized Sampled-Data Hold Functions" (GSHF) are used in the Constrained Structure Control (CSC) of periodic systems. For clarity, we first consider the case of a single system. An algorithm for finding a generalized sampled-data hold function to achieve pole assignment or optimal noise rejection is proposed. The solution is nonunique. The freedom is used for simultaneous pole assignment or optimal noise rejection in several systems. Some examples are given.