Sliding order and sliding accuracy in sliding mode control

Arie Levant*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The synthesis of a control algorithm that stirs a nonlinear system to a given manifold and keeps it within this constraint is considered. Usually, what is called sliding mode is employed in such synthesis. This sliding mode is characterized, in practice, by a high-frequency switching of the control. It turns out that the deviation of the system from its prescribed constraints (sliding accuracy) is proportional to the switching time delay. A new class of sliding modes and algorithms is presented and the concept of sliding mode order is introduced. These algorithms feature a bounded control continuously depending on time, with discontinuities only in the control derivative. It is also shown that the sliding accuracy is proportional to the square of the switching time delay.

Original languageEnglish
Pages (from-to)1247-1263
Number of pages17
JournalInternational Journal of Control
Issue number6
StatePublished - Dec 1993
Externally publishedYes


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