The ultimate bounds of equivalent control based sliding-mode control systems with short sampling time

Almost all of control systems proposed so far have been designed in the continuous-time domain. Actual systems, however, have been implemented in the discrete-time domain since microprocessors have been used for the controller, 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. The ultimate error is shown to be related in the sampling period.