Some robust finite-time sliding reachability conditions and application to nonlinear observer

In sliding mode control and estimation, an effective way of enhancing its disturbance rejection property while reducing chatter and improving transient and steady state performances is to search for appropriate sliding reachability conditions (reaching laws). This paper presents two new continuous reachability conditions with finite reaching time. Compared with other alternatives, both analysis and simulation show that they are stronger in disturbance rejection, faster in response, prominently low in overshoot, better steady state performance and chatter-free. Their performances are tested further by applying them to second order observers. Stability analysis and simulation of those observers are also provided.