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New LMI Conditions for Reduced-order Observer of Lipschitz Discrete-time Systems: Numerical and Experimental Results

  • Noussaiba GasmiEmail author
  • Assem Thabet
  • Mohamed Aoun
Research Article

Abstract

The objective of this paper is to propose a reduced-order observer for a class of Lipschitz nonlinear discrete-time systems. The conditions that guarantee the existence of this observer are presented in the form of linear matrix inequalities (LMIs). To handle the Lipschitz nonlinearities, the Lipschitz condition and the Young′s relation are adequately operated to add more degrees of freedom to the proposed LMI. Necessary and sufficient conditions for the existence of the unbiased reduced-order observer are given. An extension to H performance analysis is considered in order to deal with H asymptotic stability of the estimation error in the presence of disturbances that affect the state of the system. To highlight the effectiveness of the proposed design methodology, three numerical examples are considered. Then, high performances are shown through real time implementation using the ARDUINO MEGA 2560 device.

Keywords

Reduced-order observer discrete-time systems Lipschitz systems H performance analysis ARDUINO MEGA 2560 device 

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Copyright information

© Institute of Automation, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Research Center for Automatic Control of Nancy, CRAN-CNRS UMR 7039University of LorraineCosnes et RomainFrance
  2. 2.Modeling, Analysis and Control of Systems (MACS) Laboratory, National Engineering School of GabesUniversity of GabesGabesTunisia

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