Model Reference Discrete-Time Sliding Mode Control With Practical Prescribed-Step Stability: Theory and Applications

This article proposes a novel model reference discrete-time sliding mode control (DSMC) scheme to ensure practical prescribed-step stability for discrete-time systems. First, a tuning function-based reaching law is designed to guarantee that the sliding variable converges within user-defined steps, independent of initial conditions. In contrast to existing fixed/prescribed-step DSMC methods that rely on conservative or multiparameter-dependent upper bounds for convergence, the proposed scheme features a bound that depends on a single user-defined parameter. Then, by applying this reaching law with an optimally designed tuning function to a disturbance-free reference model, a smoothed reference trajectory is generated to mitigate the effects of past disturbances. This trajectory is then integrated into the final controller design to enhance overall system robustness. Theoretical analysis demonstrates that the sliding variable converges to the quasi-sliding mode band within the prescribed step count, and the actual number of convergence steps is close to the prescribed value. Last, simulation and experimental results verify the improved transient performance and robustness of the proposed control strategy.