Exact differentiation of signals with unbounded higher derivatives

Arie Levant*, Miki Livne

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

122 Scopus citations


Arbitrary-order homogeneous differentiators based on high-order sliding modes are generalized to ensure exact robust kth-order differentiation of signals with a given functional bound of the(κ+1) th derivative. The asymptotic accuracies in the presence of noises and discrete sampling are estimated. The results are applicable for the global observation of system states with unbounded dynamics. Computer simulation demonstrates the applicability of the modified differentiators.

Original languageEnglish
Article number6060865
Pages (from-to)1076-1080
Number of pages5
JournalIEEE Transactions on Automatic Control
Issue number4
StatePublished - Apr 2012


  • High-order sliding mode
  • homogeneity
  • nonlinear observers
  • robustness


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