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Observer Design for Discrete-Time Switching Nonlinear Models

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Hybrid Dynamical Systems

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 457))

Abstract

Switched systems are often described by continuous and discrete dynamics as well as their interactions. Although results are available for linear switching systems, for nonlinear switching models few results exist. In this chapter, we consider observer design for discrete-time switching nonlinear systems with a Takagi–Sugeno representation. For designing the observers, a switching nonquadratic Lyapunov function is used. Such Lyapunov functions have shown a real improvement of the design conditions for discrete-time Takagi–Sugeno models. The Lypunov function can be defined for each subsystem or just for the moments when switching takes place. In the first case the results are more general, but also more conservative. The second case represents a significant improvement for periodic models. Thanks to the Lyapunov function used, it is possible to design observers for some switching systems with unobservable subsystems. The developed conditions are formulated as linear or bilinear matrix inequalities. Their advantages and shortcomings are illustrated on numerical examples.

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Notes

  1. 1.

    Throughout this chapter, computed values are truncated to two decimal places.

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Authors and Affiliations

  1. Department of Automation, Technical University of Cluj-Napoca, Memorandumului 28, 400114, Cluj-Napoca, Romania

    Zsófia Lendek & Paula Raica

  2. University of Valenciennes and Hainaut-Cambresis, LAMIH UMR CNRS 8201, Le Mont Houy, 59313, Valenciennes Cedex 9, France

    Jimmy Lauber & Thierry Marie Guerra

Authors
  1. Zsófia Lendek
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  2. Paula Raica
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  3. Jimmy Lauber
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  4. Thierry Marie Guerra
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Correspondence to Zsófia Lendek .

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Editors and Affiliations

  1. LAMIH CNRS UMR 8201, University of Valenciennes and Hainaut-Cambresis, Valenciennes, France

    Mohamed Djemai

  2. LAMIH UMR-CNRS 8201, University of Valenciennes and Hainaut-Cambresis, Valenciennes, France

    Michael Defoort

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Lendek, Z., Raica, P., Lauber, J., Guerra, T.M. (2015). Observer Design for Discrete-Time Switching Nonlinear Models. In: Djemai, M., Defoort, M. (eds) Hybrid Dynamical Systems. Lecture Notes in Control and Information Sciences, vol 457. Springer, Cham. https://doi.org/10.1007/978-3-319-10795-0_2

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  • DOI: https://doi.org/10.1007/978-3-319-10795-0_2

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