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

Arie Levant*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


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.

Original languageEnglish
Title of host publicationSliding Modes After the First Decade of the 21st Century
Subtitle of host publicationState of the Art
EditorsLeonid Fridman, Rafael Iriarte, Jaime A. Moreno
PublisherSpringer Berlin Heidelberg
Number of pages34
ISBN (Print)9783642221637
StatePublished - 2011

Publication series

NameLecture Notes in Control and Information Sciences
ISSN (Print)0170-8643


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