An O(T-2) boundary layer in sliding mode for sampled-data systems

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