The discrete SMC control has excellent dynamic performance and can incorporate increased output voltage level, which is a plus at the application level.
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For designing discrete time controllers, two approaches are common. The first one is the indirect one in which a continuous controller is designed for the continuous plant. Then, the obtained controller is transformed to a discrete controller using discretization methods. in the second method (the direct method), a discrete time controller is directly designed for the discrete version of the plant. The indirect method is simpler but the direct method is more precise than the indirect one. This may be the reason why the discrete time sliding mode controller gives superior performance than its continuous version.
DSMC is better than CSMC because of in CSMC switching control needs actuators to switch at infinte frequency which is not practically possible in the real world.
to remove this gap between theory and practice, discrete time SMC is developed.