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In this paper, an approach to design state-feedback gain is proposed for a class of relay control systems. The resulting controller can drive states of the systems to desired limit cycles. The design consists of two steps. First, the form of the state-feedback gain is proposed. It is proved that each gain in the proposed form can guarantee the existence and stability of a limit cycle. Then, by an exact method, the value of state-feedback gain is chosen to obtain the limit cycle with prescribed characteristics. In order to demonstrate the effectiveness, the proposed approach is applied to the attitude control of a torpedo. Simulation results show that the designed relay controller drives the state of the torpedo to a limit cycle with desired amplitude and frequency.