State estimation and quasi sliding mode control of differential LRPs

This chapter investigates the state estimation and observer-based SMC of differential LRPs. The main advantage of the proposed scheme is that it eliminates the need for the state variables and pass profile variables to be fully accessible for its control. This is possible through the use of a SMC law, which performs its control by employing the state estimates obtained from the sliding mode observer. A sufficient condition for the existence of desired observer is established in terms of an LMI. Then, an observer-based SMC law is synthesized to guarantee the stability along the pass of the overall closed-loop process composed of the observer process and the estimation error process. It is shown that the proposed SMC law based on the estimated states can guarantee that the sliding modes within both the state estimation space and the estimation error space are attained simultaneously.