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

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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.

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Authors and Affiliations

  1. Research Center for Automatic Control of Nancy, CRAN-CNRS UMR 7039, University of Lorraine, Cosnes et Romain, 54400, France

    Noussaiba Gasmi

  2. Modeling, Analysis and Control of Systems (MACS) Laboratory, National Engineering School of Gabes, University of Gabes, Gabes, 6072, Tunisia

    Noussaiba Gasmi, Assem Thabet & Mohamed Aoun

Authors
  1. Noussaiba Gasmi
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  2. Assem Thabet
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  3. Mohamed Aoun
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Correspondence to Noussaiba Gasmi.

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Recommended by Associate Editor Wing Cheong Daniel Ho

Noussaiba Gasmi received the degree in electrical and automatic engineering from National Engineering School of Gabes, Tunisia in 2014. Since 2015, she is a Ph. D. degree candidate in automatic control at Research Center for Automatic Control of Nancy, University of Lorraine, France, and the MACS Laboratory (Modeling, Analysis and Control of Systems), National Engineering School of Gabes, University of Gabes, Tunisia. Her research interests include identification, state estimation and robust control of dynamical systems.

Assem Thabet received the B. Eng. degree in electrical and automatic engineering from National Engineering School of Gabes, Tunisia in 2006, and the M. Eng. and Ph. D. degrees in automatic control from the University of Gabes, Tunisia in 2008 and 2012, respectively. Since 2012, he is an associate professor with the University of Gabes, Tunisia, and a member of the MACS Laboratory (Modeling, Analysis and Control of Systems) of National Engineering School of Gabes, Tunisia. His research interests include identification, state estimation and control of dynamical systems.

Mohamed Aoun received the Ph. D. degree in automatic control from University of Bordeaux, France in 2005. He is currently an associate professor in automatic control, electrical engineering, and computer engineering at the National Engineering School of Gabes, Tunisia, and a member of its MACS Laboratory (modeling, analysis and control of systems). His research interests include automatic control, system identification, robust state estimation, diagnosis and fractional differentiation.

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Gasmi, N., Thabet, A. & Aoun, M. New LMI Conditions for Reduced-order Observer of Lipschitz Discrete-time Systems: Numerical and Experimental Results. Int. J. Autom. Comput. 16, 644–654 (2019). https://doi.org/10.1007/s11633-018-1160-9

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  • DOI: https://doi.org/10.1007/s11633-018-1160-9

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