The ultimate bound of discrete sliding mode control system for the sampled-data system with short sampling time under the existence of constant disturbance

Almost all of control systems proposed so far have been designed in the continuous-time domain. In the actual system, however, a control system has been implemented in the discrete-time domain since microprocessors and/or MCU have been used for the controllers, that is, the overall system turned to be a sampled-data system. In this case, the ultimate error and/or steady state 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 second-order sampled data system with the short sampling time has been investigated under the existence of a constant external disturbance. The ultimate error is shown to be bounded and is related in the sampling period.