Analysis of chattering in sliding mode control systems with continuous boundary layer approximation of discontinuous control

It has been a widely accepted notion that approximation of discontinuous control by certain continuous function in a boundary layer results in chattering elimination in sliding mode (SM) control systems. It is shown through three different types of analysis that in the presence of parasitic dynamics, this approach to chattering elimination would work only if the slope of the continuous nonlinear function within the boundary layer is low enough, which may result in the deterioration of performance of the system. A few examples are provided.