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Variable structure control design for uncertain discrete systems with time-delays

In this paper, the design of variable structure control (VSC) for uncertain discrete systems with time-delays is considered. The original uncertain discrete system with time-delay is simplified to uncertain discrete system without time-delay. Using exponential reaching law, the reason of causing uncertain discrete system without time-delay chattering is given, and using boundary layer, an improved discrete reaching law is developed. By this method, the reaching time is shortened, and it can drive the system to reach the switching surface in finite time and remain on it. The switching surface will not be passed through, so the chattering is eliminated. This method guarantees the stability of the systems.