In this study, a simple hyperplane design method based on the discrete‐time Riccati equation is proposed, and the inter‐relations are investigated for the basic requirement on sliding surface selection, the assumption of stabilisability, the Riccati inequality and the standard Riccati equation. A state and disturbance observer is embedded in discrete‐time sliding mode control (DSMC) to achieve its applicability when only partial system states can be measured. In order to improve the performance of the system in control updating times, a novel event‐triggered DSMC with a state and disturbance observer is proposed. It is shown that the proposed method achieves a quasi sliding mode with a small boundary layer. Simulation examples are presented to show the effectiveness and advantages of the proposed design schemes.