Chattering Analysis

A formal mathematical definition of chattering is proposed. Chattering phenomena are classified into three types. In particular, the first type is harmless and cannot be avoided. Chattering properties of various control approaches are considered. The dangerous second and third types of chattering phenomena are proved to be removable by proper use of high-order sliding-modes (HOSM). Fast stable actuators and sensors only generate the first type of chattering in HOSM systems and practically never affect the sliding motion. Computer simulation confirms the theoretical results.