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A control system design for two-inertia resonant systems that takes account of shaft torsion is proposed. On the basis of elementary knowledge of material mechanics and the ASME code, we derive an inequality condition for avoiding metal fatigue of a shaft. To satisfy the derived condition as well as other design specifications, a feedback controller is designed using the LMI-based H2 synthesis on the basis of the critical control concept. The disturbance observer is also used to recover the nominal property of the plant. An illustrative design example using a laboratory test bed shows that the amount of shaft torsion remains within the acceptable level for fatigue avoidance.