An O(T2) boundary layer in sliding mode for sampled-data systems

The use of a discontinuous control law (typically, sign functions) in a sampled-data system will bring about chattering phenomenon in the vicinity of the;sliding manifold, leading to a boundary layer with thickness O(T), where T is the sampling period. However, by proper consideration of the sampling phenomenon in the discrete-time sliding mode control design, the thickness of the boundary layer can be reduced to O(T-2). In contrast to discontinuous control for continuous-time VSS, the discrete-time sliding mode control need not be of switching type.