High-Gain Nonlinear Observer With Lower Tuning Parameter

Ali Zemouche, Fan Zhang, Frédéric Mazenc, Rajesh Rajamani

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33 Scopus citations


This paper develops a new high-gain observer design method for nonlinear systems that has a lower gain compared to the standard high-gain observer. This new observer, called HG/LMI observer, is obtained by combining the standard high-gain methodology with the LMI-based observer design technique. Through analytical developments, this paper shows how the new observer provides lower gains, shows how it applies to systems with multinonlinear functions, and analyzes performance in the presence of measurement noise and/or delayed output measurements. A numerical example is given to illustrate the increasing advantage of the new HG/LMI observer with increase in the observer's 'compromise index.' Finally, the applicability and performance of the observer is demonstrated for a real-world application consisting of a train's magnetic levitation system.

Original languageEnglish (US)
Article number8540946
Pages (from-to)3194-3209
Number of pages16
JournalIEEE Transactions on Automatic Control
Issue number8
StatePublished - Aug 2019

Bibliographical note

Funding Information:
Manuscript received April 26, 2018; revised May 1, 2018 and October 9, 2018; accepted October 18, 2018. Date of publication November 20, 2018; date of current version July 26, 2019. The work of F. Zhang was supported in part by the State Key Laboratory of Intelligent Control and Decision of Complex Systems, in part by the National Natural Science Foundation of China under Grant 61703099, and in part by the China Postdoctoral Science Foundation under Grant 2017M621589. The work of R. Rajamani was supported by the NSF Grant CMMI 1562006. Recommended by Associate Editor M. Alamir. (Corresponding author: Rajesh Rajamani.) A. Zemouche is with the University of Lorraine, CRAN CNRS UMR 7039, Cosnes-et-Romain 54400, France, and also with the EPI Inria DISCO, Laboratoire des Signaux et Systémes, CNRS–CentraleSupélec, Gif-sur-Yvette 91192, France (e-mail:,ali.zemouche@univ-lorraine.fr).

Publisher Copyright:
© 2018 IEEE.


  • High-gain methodology
  • LMIs
  • Lipschitz systems
  • observer design


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