I. Introduction
The design problem of state observer using sliding mode control theory has been studied for a long time. A primary advantage of sliding mode method in observation for dynamical systems is their natural robustness to unmodelled dynamics provided sliding conditions are maintained. Sliding mode observer (SMO) for continuous-time systems appeared in early work for linear systems [1]–[3], and have been gradually extended to nonlinear systems [4], [5]. Over the last two decades, discrete-time sliding mode observers (DSMO) have been developed. In [6], the concept of sliding lattice for discrete-time systems was introduced and DSMO was designed for SISO linear systems using Lyapunov min-max method, and the discrete-time sliding mode is shown to exist if sliding points finally lie in a boundary layer. So far, sliding mode controllers for discrete-time linear systems [7]–[9] as well as contributions to nonlinear control problems [10] have made great progress. However, DSMO has gotten ahead slowly, let alone DSMO for nonlinear uncertain systems. Even if some are about nonlinear systems, they are mostly for a specified system or based on state transformations, which cannot spread to other systems easily. Besides, general sliding mode approach only has robustness to matched uncertainties, and chattering phenomena which is a notorious effects in variable structure systems (VSSs), limit the employment of SMO extremely. In order to deal with these problems, a novel DSMO design strategy based on sliding mode prediction (SMP) is presented in this paper. Because of the existence of sliding mode surface, the observer has strong robustness. Due to SMP model, the observer can use future information of sliding mode.