System configuration of smoothed and differential values estimator by using linear and sliding mode system

We have proposed the new nonlinear filter to estimate the smoothed and differential values by using sliding mode system (ESDS). It works very effectively to eliminate the impulse noise by keeping the sudden shift of the signals. In order to construct ESDS, it requires the system that is globally uniform and asymptotically stable at the origin. As the stable system, the minimum time system that is one of the sliding mode systems has been used. In this paper, we apply the linear system and sliding mode system that has a linear switching line as the stable system, and we clarify the validity of our theorem and configuration of ESDS.