The ultimate bound of a sampled-data sliding mode control system for second-order systems with time-varying disturbance

Although system is generated in continuous time domain, actual system is in discrete time domain because experimental devices are digital. In this reason, system is not asymptotically stable. It causes that ultimate error cannot converge to zero in finite time. So ultimate error bound is needed to inspect overall system. In previous researches, disturbance that is used to derivate ultimate error bound was constant. In this paper, disturbance is extended into time-varying one. In very short sampling time, ultimate error bound with constant disturbance are related with system that affected by time-varying disturbance.