A Time-delay Approach for Extremum Seeking of Nonlinear Static Maps

Yang Zhu*, Emilia Fridman

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review


This paper develops a constructive time-delay approach to averaging for gradient-based extremum seeking (ES) control of nonlinear static maps of non-quadratic form. Under the assumption that some prior knowledge of the nonlinear map with its derivatives is available, for the first time, we derive a quantitative analysis for ES close-loop systems with upper bounds on the tuning parameter that preserves the exponential stability and on the convergence error of extremum seeking. By transforming the ES system into a time-delay neutral type system with distributed delays, the developed method gives an accurate perturbed system of ES without employing any approximate calculation, and suggests a direct Lyapunov-Krasovskii approach in the form of linear matrix inequalities (LMIs), for the transformed time-delay plant to derive efficient stability conditions .

Original languageEnglish
Pages (from-to)258-263
Number of pages6
Issue number1
StatePublished - 1 Jan 2023
Event12th IFAC Symposium on Nonlinear Control Systems, NOLCOS 2022 - Canberra, Australia
Duration: 4 Jan 20236 Jan 2023


  • Extremum Seeking
  • Non-quadratic
  • Nonlinear
  • Static
  • Time-delay


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