Scope of the Theory of Sliding Modes

A number of processes in mechanics, electrical engineering, and other areas, are characterized by the fact that the righthand sides of the differential equations describing their dynamics feature discontinuities with respect to the current process state. A typical example of such a system is a dry (Coulomb) friction mechanical system whose force of resistance may take up either of the two sign-opposite values depending on the direction of the motion. This situation is often the case in automatic control systems where the wish to improve the system performance, minimize power consumed for the control purposes, restrict the range of possible variations of control parameters, etc. leads to controls in the form of discontinuous functions of the system state vector and the system input actions.