ABSTRACT
The control action switches at high frequency should the sliding mode occur in the system. Sliding modes as a phenomenon may appear in a dynamic system governed by ordinary differential equations with discontinuous right-hand sides. The term sliding mode first appeared in the context of relay systems. It may happen that the control as a function of the system state switches at high frequency, and this motion is called sliding mode. Formally, sliding mode may appear not only in a control system with discontinuous control but in any dynamic system with discontinuities in the motion equations. The ideas underlying modern analysis and design methods for “sliding mode control” may be found in the publications of the 1930s. Sliding modes became a principle operation mode in variable structure systems or systems consisting of a set of continuous subsystems with a proper switching logic.
