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Sampled-data control systems for linear multivariable plants subjected to disturbing signals are considered. The regulator problem (rejection of effects of disturbing signals in the outputs without taking into consideration command-output transfer functions) is treated first. Then the servo problem (rejection of disturbances and realization of a desired over-all transfer function) is treated as an extension of the regulator problem. It is shown that one of the conditions for obtaining total rejection of the disturbing signals leads to a diagonalization of the disturbance transmission matrix. Then the multivariable problem is reduced to a certain number of single-variable problems. Although any of the well-known techniques used in the design of single-variable control problems can be extended to solve those problems, only an extension of the optimum design through digital compensation is presented in this paper.