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Design of Polynomial Observer-Based Fault-Tolerant Controller for Polynomial Systems with State Delay: A Sum of Squares Approach

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Abstract

This paper investigates both fault estimation and fault-tolerant control problems for polynomial systems with state delay in presence of faults. Before studying the control problem, a polynomial observer is proposed to jointly estimate state and fault vectors. Based on the obtained informations, a polynomial controller is designed to compensate fault effects and to stabilize the closed-loop systems even in presence of state delay. The existence of both polynomial observer and controller is proved via satisfying sufficient conditions based on a sum of square (SOS) approach. Polynomial observer and controller gains are computed using SOSTOOLS. Finally, a numerical example is given to demonstrate that the SOS approach provides a significant improvement in reaction to fault occurrence for time delay systems. Furthermore, a tunnel diode circuit and a mass–spring–damper system are used to illustrate the applicability of the design method.

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Authors and Affiliations

  1. Laboratory of Sciences and Techniques of Automatic Control and Computer Engineering (Lab-STA), National Engineering School of Sfax (ENIS), University of Sfax, Sfax, Tunisia

    Abderrahim Messaoudi, Hamdi Gassara & Salama Makni

  2. Modeling, Information, and Systems Laboratory (MIS), University of Picardie Jules Verne, UFR des Sciences, 33 Rue St Leu, 80000, Amiens, France

    Ahmed El Hajjaji

Authors
  1. Abderrahim Messaoudi
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  2. Hamdi Gassara
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  3. Salama Makni
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  4. Ahmed El Hajjaji
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Correspondence to Ahmed El Hajjaji.

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Messaoudi, A., Gassara, H., Makni, S. et al. Design of Polynomial Observer-Based Fault-Tolerant Controller for Polynomial Systems with State Delay: A Sum of Squares Approach. Circuits Syst Signal Process 41, 3153–3171 (2022). https://doi.org/10.1007/s00034-021-01946-9

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  • DOI: https://doi.org/10.1007/s00034-021-01946-9

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