Sliding mode order and accuracy in sliding mode adaptation and convergence acceleration

Yaniv Dvir*, Arie Levant

*Corresponding author for this work

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

4 Scopus citations


Fundamental properties of Sliding Mode (SM) Control (SMC) are considered. The best and worst possible SM accuracy of Single-Input Single-Output (SISO) and Multi-Input Multi-Output (MIMO) systems is shown to be directly determined by the number of continuous derivatives of the sliding variables. The best SM accuracy is obtained in the both SISO and MIMO cases by homoneous SMs. SM adaptation is to be based on the detection of a real SM. Such detection is based on the observation of the above best possible accuracy in the presence of noises and discrete sampling. Convergence to SM is accelerated by control, which is piecewise homogeneous on successive time segments. It allows feedback application of homogeneous SM-based differentiators with piece-wise constant parameters, providing for arbitrarily fast convergence and preserving the optimal accuracy featuring homogeneous SMs. Simulation results show the feasibility of the proposed methods and demonstrate their asymptotic accuracy.

Original languageEnglish
Title of host publicationStudies in Systems, Decision and Control
PublisherSpringer International Publishing
Number of pages25
StatePublished - 2015

Publication series

NameStudies in Systems, Decision and Control
ISSN (Print)2198-4182
ISSN (Electronic)2198-4190


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