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A general analytical technique described in this paper permits the extension of -transform methods to sampled-data systems containing synchronized switches which do not operate with the same sampling rate. Sampling periods of each switch are first expressed in the form (where are integers not equal to zero) and then it is shown that each switch with a period can be replaced by a system of switches and advance and delay elements where each switch operates with a sampling period . In this way, the original sampled-data system can be represented by an equivalent system containing switches operating with the same sampling rate. The general solution of such equivalent systems is outlined in this paper.