Chattering-free condition for sliding mode control with unidirectional auxiliary surfaces

A chattering-free condition is proposed as a sufficient condition for the sliding mode control with unidirectional auxiliary surfaces (UAS-SMC) strategy in a class of non-linear systems. With this condition, the UAS-SMC controller would enjoy the following properties: 1) chattering-free property of the control input; 2) enhanced approaching speed on the switching surfaces (except the original point); 3) no requirement to measure the derivatives; 4) a positively invariant set formed by UAS. The stability of the closed-loop system is demonstrated with a chattering-free UAS-SMC controller. Numerical simulation is given to illustrate the benefits and properties of the proposed controller and algorithm