Discrete-time sliding mode control for nonlinear systems with unmatched uncertainties and uncertain control vector

This paper presents a technique for control system design that provides robust stability. in the presence of bounded modeling errors. The proposed method is a discrete-time? version of a well known sliding mode control technique with saturation functions that generates the boundary layer without requiring either matched uncertainties or smooth functions. It is shown that the boundary layer can be made attractive and that the boundary layer thickness is bounded under mild conditions. It is also shown that asymptotic stability can De guaranteed if the available model is assumed to be perfect. An example is used to illustrate the proposed design technique.