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Hybrid Dynamical Systems pp 261–275Cite as

Continuous–Discrete-Time Observers for a Class of Uniformly Observable Systems

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

Abstract

This chapter addresses the observer design problem for a class of continuous-time dynamical systems with nonuniformly sampled measurements. More specifically, an observer is proposed that runs in continuous-time with an output error correction term that is updated in a mixed continuous-discrete fashion. The proposed observer is actually an impulsive system as it is described by a set of differential equations with instantaneous state impulses corresponding to the measured samples and their estimates. In addition, it is shown that such an impulsive system can be put under the form of a hybrid system composed of a continuous-time high gain observer coupled with an inter-sample output predictor. The proposed observer present two design features that are worth noting: First, the observer calibration is achieved through the tuning of a scalar design parameter. Second, the exponential convergence to zero of the observation error is established under a well-defined condition on the maximum value of the sampling partition diameter. Simulations results dealing with a flexible joint robot arm are given in order to highlight the performance of the proposed observer.

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Author information

Authors and Affiliations

  1. GREYC Laboratory (UMR 6072 CNRS), Université de Caen and ENSICAEN, 6 Bd Maréchal Juin, 14050, Caen Cedex, France

    Mondher Farza & Mohammed M’Saad

  2. Engineering and Environment, Northumbria University, Newcastle upon Tyne, NE1 8ST, UK

    Krishna Busawon

Authors
  1. Mondher Farza
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  2. Mohammed M’Saad
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  3. Krishna Busawon
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Corresponding author

Correspondence to Krishna Busawon .

Editor information

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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Farza, M., M’Saad, M., Busawon, K. (2015). Continuous–Discrete-Time Observers for a Class of Uniformly Observable Systems. 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_10

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  • DOI: https://doi.org/10.1007/978-3-319-10795-0_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-10794-3

  • Online ISBN: 978-3-319-10795-0

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