Higher order sliding: Differentiation and black-box control

A. Levant*

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

20 Scopus citations


Sliding modes describe motions on discontinuity sets of dynamic systems and are provided by a persistent system switching with theoretically infinite frequency. The standard sliding modes are applicable to control output variables with relative degree 1. Having preserved or generalized the main properties of standard sliding mode, higher order sliding modes (HOSM) may be applied with any relative degree and, when properly used, totally remove the chattering effect. That allows full real-time control of the output variables, when only the relative degree of the dynamic system is known, and the system is actually considered as a "black box". The HOSM controllers being based on the use of real-time higher-order output derivatives, robust exact differentiation becomes the key problem of the HOSM theory. Fortunately, the HOSM technique may also be applied to solve the differentiation problem. Differentiation usage in HOSM control is demonstrated by computer simulation of model and real-life examples.

Original languageEnglish
Pages (from-to)1703-1708
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
StatePublished - 2000
Externally publishedYes
Event39th IEEE Confernce on Decision and Control - Sydney, NSW, Australia
Duration: 12 Dec 200015 Dec 2000


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