Study of reaching law approach for discrete-time variable structure control system

The reaching law approach, which is widely used in discrete-time variable structure controller design, is thoroughly studied in a new point of view. Based on the new concept “Ideal reaching law” and “Robust reaching law” proposed here, the reaching laws can be classified as two types. The mechanisms of robust controller design based on these two types of reaching laws are different. These similarities and differences are analyzed so that the confusions and misapprehends of reaching law approach can be clarified. Ideal reaching law is a type of desired ideal sliding mode motion dynamics without taking system uncertainties into account, so an additional term, such as bound value of uncertainties or disturbance estimator, is necessary to ensure the closed-loop system to be robust stable. However, robust reaching law is a type of desired robust sliding mode motion dynamics with taking robustness property into account by reaching law itself. This means that an additional term will induce seriously chattering due to over compensation, as conventional discrete reaching law approach does.