A decoupled design of a robust sliding mode observer

In this paper, we propose a decoupled approach to the design of a robust sliding mode observer. The proposed observer has a linear part, which is designed based on the linear observer theory, and a discontinuous part based on the sliding mode technique to reject the disturbance signals. Here, the discontinuous injection of output error is fed only to the sliding mode part of the observer, whereas the linear part is designed with the linear injection of output error. We state the sufficient condition which guarantees the existence of the proposed sliding mode observer. The main outcome of this design is that the steady-state accuracy of the observer is improved from that of the existing ones, where the full order discontinuous output error vector is injected into the observer dynamics. These switching terms in discrete dynamics often result in numerical chattering, which is attenuated in our proposed observer. We also show the global convergence of estimation error for this observer in the presence of disturbance. Finally, we demonstrate the design technique of the proposed sliding mode observer with an example.