A state-dependent boundary layer design for sliding mode control

The use of a boundary layer in sliding-mode control has been a common technique to reduce chattering of the control signal. However, different choices of the boundary layer width lead to conflicting effects: a large/small boundary layer width can more/less effectively alleviate the chattering phenomenon, but leads to less/more accurate control results. This note proposes online adjusting the width of the boundary layer based on the state norm for an uncertain linear system. The proposed state-dependent boundary layer design can effectively eliminate chattering while at the same time ensuring almost perfect control accuracy.