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A stability criterion for feedback systems with a linear time-invariant forward loop and a periodically time-varying gain in the feedback loop is developed. As most recent frequency-domain stability criteria, it requires the existence of a multiplier having certain properties. A graphic technique is given to determine whether or not this multiplier exists. The proof of the criterion is based on the Floquet theory and the classical theory of Toeplitz forms. Examples to illustrate the criterion are included.