The ultimate bound of a sampled-data sliding mode control system with short sampling period

Almost all of control methods proposed so far have been designed in the continuous-time domain. Actual systems, however, have been implemented in the discrete-time domain since MCU and/or microprocessors have been used for the control system, that is, the overall system turned to be a sampled-data system. In this case, 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 has been investigated. The ultimate error is shown to be related in the sampling period.