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On Robust Pseudo State Estimation of Fractional Order Systems

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Positive Systems (POSTA 2016)

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 471))

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Abstract

The goal of this chapter is to design robust observers for fractional dynamic continuous-time linear systems described by pseudo state space representation. The fractional observer is guaranteed to compute a domain enclosing all the system pseudo states that are consistent with the model, the disturbances and the measurement noise realizations. Uncertainties on the initial pseudo state and noises are propagated in a reliable way to estimate the bounds of the fractional pseudo state. Only the bounds of the uncertainties are used and no additional assumptions about their stationarity or ergodicity are taken into account. A fractional observer is firstly built for a particular case where the estimation error can be designed to be positive. Then, the general case is investigated through changes of coordinates. Some numerical simulations illustrate the proposed methodology.

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Notes

  1. 1.

    The order relations \(<, \le , >, \ge \) should be understood componentwise throughout this chapter.

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Acknowledgements

This work was developed within the “Research in Paris” project supported by the city of Paris.

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Authors and Affiliations

  1. Conservatoire National des Arts et Métiers, Cedric-Lab, 292, Rue St-Martin, 75141, Paris, France

    Tarek Raïssi

  2. Research Laboratory Modeling, Analysis and Control Systems, National Engineering School of Gabes, Street Omar Ibn El Khattab - Zerig, 6029, Gabes, Tunisia

    Mohamed Aoun

Authors
  1. Tarek Raïssi
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Correspondence to Tarek Raïssi .

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Editors and Affiliations

  1. Università Campus Biomedico , Rome, Italy

    Filippo Cacace

  2. Sapienza Università di Roma , Rome, Italy

    Lorenzo Farina

  3. Università Campus Biomedico , Rome, Italy

    Roberto Setola

  4. Università dell’Aquila , L'Aquila, Italy

    Alfredo Germani

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Raïssi, T., Aoun, M. (2017). On Robust Pseudo State Estimation of Fractional Order Systems. In: Cacace, F., Farina, L., Setola, R., Germani, A. (eds) Positive Systems . POSTA 2016. Lecture Notes in Control and Information Sciences, vol 471. Springer, Cham. https://doi.org/10.1007/978-3-319-54211-9_8

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  • DOI: https://doi.org/10.1007/978-3-319-54211-9_8

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