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Robust Σ–Δ modulation-based sliding mode observers for linear systems subject to time polynomial inputs

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  • Hebertt Sira-Ramírez
  • Vicente Feliu Batlle

Abstract

In this article, we propose the use of Σ–Δ modulation-based sliding mode observers undergoing switched output injections as in remote state estimation cases. The class of switched observers, treated here, inherit their robustness with respect to un-modelled classical perturbation inputs of the polynomial type affecting the observed plant, from that of an average (non-discontinuous) observer design exhibiting dynamic output reconstruction error injections. These extended output injections consist of linear combinations of a sufficient number of iterated integrals of the output estimation error. In achieving the required robustness behaviour with respect to classical perturbations, a suitable and natural dualisation of Generalised Proportional Integral control is being used. The proposed observers are shown to be useful in collision detection schemes for flexible robotics.

Suggested Citation

  • Hebertt Sira-Ramírez & Vicente Feliu Batlle, 2011. "Robust Σ–Δ modulation-based sliding mode observers for linear systems subject to time polynomial inputs," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(4), pages 621-631.
    • Handle: RePEc:taf:tsysxx:v:42:y:2011:i:4:p:621-631
    DOI: 10.1080/00207720903072241
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