The ultimate bound of a sampled-data system with sliding mode controller

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. For the sampled-data system, it is well known that the ultimate error cannot converge to zero even though the proposed continuous-time control algorithm showed the asymptotic stability in the continuous-time domain. That is, the actual output turns to be a bounded signal in the steady state. In this paper, therefore, the ultimate error bound of the sampled-data system has been derived, and it is shown that the ultimate error is related to the sampling period. It represents that one can easily obtain the sampling period enough to get the desired steady state error bound.