On Robust Pseudo State Estimation of Fractional Order Systems

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


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.


Fractional systems Interval observers Robust estimation 



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


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Conservatoire National des Arts et MétiersParisFrance
  2. 2.Research Laboratory Modeling, Analysis and Control SystemsNational Engineering School of GabesGabesTunisia

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