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On Discontinuous Observers for Second Order Systems: Properties, Analysis and Design

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Advances in Sliding Mode Control

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 440))

Abstract

Smooth observers are able to converge asymptotically to the actual value of the state, in the case where no measurement noise and no persistently acting perturbations are present. Under the same conditions continuous observers can converge in finite time. However, they are unable to converge if a perturbation/ uncertainty is present. In order to achieve finite time and exact convergence in the presence of perturbations, it is necessary to use discontinuous injection terms. In this chapter, some recent developments in this direction for second order systems will be presented and the results will be illustrated by means of simple examples. It will be also shown that by including non globally Lipschitz injection terms the convergence time of the observers can be made independent of the initial condition. The restriction to the two dimensional case is due to the fact that all proofs are done by means of Lyapunov functions, that are only available for planar systems. However, this has as advantage that the treatment is mainly tutorial, and provides on the one side an easy introduction to the topic, and on the other side it presents in the simplest case the main results that are (probably) valid for the general case. We hope to be able to provide a similar treatment of the general case in the near future.

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Authors and Affiliations

  1. Eléctrica y Computación, Instituto de Ingeniería, Universidad Nacional Autónoma de México, 04510, Mexico D.F., Mexico

    Jaime A. Moreno

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  1. Jaime A. Moreno
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Correspondence to Jaime A. Moreno .

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Editors and Affiliations

  1. , Interdisciplinary Programme in Systems, Indian Institute of Technology Bombay, ACRE Building 114 B, Mumbai, 400 076, Maharashtra, India

    B Bandyopadhyay

  2. , Dept. of Electrical Engineering, Indian Institute of Technology Delhi, Room No : II/335, New Delhi, 110 016, India

    S Janardhanan

  3. , Department of Electronics, University of Kent, Jennison Building - Room 1.54, Kent, CT2 7NT, United Kingdom

    Sarah K. Spurgeon

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Moreno, J.A. (2013). On Discontinuous Observers for Second Order Systems: Properties, Analysis and Design. In: Bandyopadhyay, B., Janardhanan, S., Spurgeon, S. (eds) Advances in Sliding Mode Control. Lecture Notes in Control and Information Sciences, vol 440. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36986-5_12

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  • DOI: https://doi.org/10.1007/978-3-642-36986-5_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-36985-8

  • Online ISBN: 978-3-642-36986-5

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