Sliding mode control design based on Ackermann´s formula

The sliding mode control methods are developed to design systems which have the desired dynamic behavior and are robust with respect to perturbations. It is shown that the discontinuity plane for sliding mode control may be found in an explicit form using Ackermann´s formula. Two design procedures are derived. First, static controllers are designed to enforce sliding modes with the desired dynamic properties after a finite-time interval. Then, dynamic controllers are designed that exhibit the desired dynamic properties during the entire control process