Finite-time stability and high relative degrees in sliding-mode control

Establishing and exactly keeping constraints of high relative degrees is a central problem of the modern sliding-mode control. Its solution in finite-time is based on so-called high-order sliding modes, and is reduced to finite-time stabilization of an auxiliary uncertain system. Such stabilization is mostly based on the homogeneity approach. Robust exact differentiators are also developed in this way and are used to produce robust output-feedback controllers. The resulting controllers feature high accuracy in the presence of sampling noises and delays, ultimate robustness to the presence of unaccounted-for fast stable dynamics of actuators and sensors, and to small model uncertainties affecting the relative degrees. The dangerous types of the chattering effect are removed artificially increasing the relative degree. Parameters of the controllers and differentiators can be adjusted to provide for the needed convergence rate, and can be also adapted in real time. Simulation results and applications are presented in the fields of control, signal and image processing.