Sampled-Data Extremum Seeking with Constant Delay: A Time-Delay Approach

Yang Zhu*, Emilia Fridman, Tiago Roux Oliveira

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


This article proposes a constructive method for sampled-data extremum seeking (ES) with square wave dithers and constant delays, by using two time-delay approaches: one to averaging and the other to sampled-data control. We consider gradient-based ES for static maps which are of quadratic forms. By transforming the ES system to the time-delay system, we have developed a stability analysis via a Lyapunov-Krasovskii method. We derive the practical stability conditions in terms of linear matrix inequalities for the resulting time-delay system. The time-delay approach offers a quantitative calculation on the upper bound of the dither and sampling periods, constant delays that the ES system is able to tolerate, as well as the ultimate bound of the extremum seeking error. This is in the presence of uncertainties of extremum value and extremum point.

Original languageEnglish
Pages (from-to)432-439
Number of pages8
JournalIEEE Transactions on Automatic Control
Issue number1
StatePublished - 1 Jan 2023


  • Sampled-data
  • extremum seeking
  • time-delay


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