Almost all of control schemes proposed so far have been designed in the continuous-time domain theoretically. Actual systems, however, have been implemented in the discrete-time domain since Micro Control Unit(MCU) and/or microprocessors have been used for the controllers. Thus, the overall system turned to be a sampled-data system, and generally speaking, the ultimate error cannot converge to zero in the actual system even though the proposed control algorithm showed the asymptotic stability in the continuous-time domain. In this paper, therefore, the ultimate error bound of a sampled data system with a short sampling period has been investigated. The ultimate error is shown to be related in the sampling period.