Circle criterion-based ℋ observer design for Lipschitz and monotonic nonlinear systems – Enhanced LMI conditions and constructive discussions

Ali Zemouche, Rajesh Rajamani, Gridsada Phanomchoeng, Boulaïd Boulkroune, Hugues Rafaralahy, Michel Zasadzinski

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53 Scopus citations


A new LMI design technique is developed to address the problem of circle criterion-based ℋ observer design for nonlinear systems. The developed technique applies to both locally Lipschitz as well as monotonic nonlinear systems, and allows for nonlinear functions in both the process dynamics and output equations. The LMI design condition obtained is less conservative than all previous results proposed in the literature for these classes of nonlinear systems. By judicious use of a modified Young's relation, additional degrees of freedom are included in the observer design. These additional decision variables enable improvements in the feasibility of the obtained LMI. Several recent results in the literature are shown to be particular cases of the more general observer design methodology developed in this paper. Illustrative examples are given to show the effectiveness of the proposed methodology. The application of the method to slip angle estimation in automotive applications is discussed and experimental results are presented.

Original languageEnglish (US)
Pages (from-to)412-425
Number of pages14
StatePublished - Nov 2017

Bibliographical note

Funding Information:
He has co-authored over 120 journal papers and is a co-inventor on 13 patent applications. He is the author of the popular book “Vehicle Dynamics and Control” published by Springer Verlag. He has served as Chair of the IEEE Technical Committee on Automotive Control and on the editorial boards of the IEEE Transactions on Control Systems Technology, the IEEE/ASME Transactions on Mechatronics, and the IEEE Control Systems Magazine. He is a fellowof ASME and has been a recipient of the CAREER award from the National Science Foundation, the 2001 Outstanding Paper award from the journal IEEE Transactions on Control Systems Technology , the Ralph Teetor Award from SAE, and the 2007 O. Hugo Schuck Award from the American Automatic Control Council.

Publisher Copyright:
© 2017 Elsevier Ltd


  • LMI approach
  • Lipschitz systems
  • Observers design
  • Slip angle estimation
  • ℋ synthesis


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