Variable structure control for multi-input discrete uncertain systems with control delay

The variable structure control for multi-input discrete uncertain systems with control delay is studied. The original discrete uncertain system with control delay is simplified to a discrete uncertain system without time-delay, and a novel variable structure control strategy for the discrete uncertain system is developed. When the uncertainty change is slow, the sliding mode is achieved with this control strategy, which drives the system to reach and remain in the neighborhood about the intersection of a set of prescribed sliding manifolds in finite time, and then asymptotically reach the equilibrium point. The simulation results prove the validity of the proposed approach.