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A Method of Estimating the Domain of Attraction for Nonlinear Discrete-Time Systems

  • Research Article - Electrical Engineering
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Abstract

This paper investigates the problem of estimating an asymptotic stability region of nonlinear polynomial discrete-time systems. To achieve an appropriate estimation of subsets of attraction regions for asymptotically stable equilibrium points, the reverse trajectory formalism is applied through the formulation of iterative algorithms. The developed methods enable us to obtain enlarged circular domains of attraction that are comparable with the ones obtained by delicate computational procedures. The main advantage of the synthesized algorithms is that they disregard the problem of constructing Lyapunov function to achieve the control target for nonlinear systems. An instructive example of a power electrical system is used as an illustration of the results of the synthesized approaches.

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Authors and Affiliations

  1. Department of Industrial Engineering, College of Engineering of Hail, Hail University, Po.Box 2440, Hail, Kingdom of Saudi Arabia

    Houssem Jerbi

  2. Laboratoire des systèmes automatisés, Polytechnic School of Tunis, Tunisia Ecole Polytechnique de Tunisie, B.P. 743-2078, La Marsa, Tunisia

    Naceur Benhadj Braiek & Anis Belhadj Brahim Bacha

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  1. Houssem Jerbi
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  2. Naceur Benhadj Braiek
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  3. Anis Belhadj Brahim Bacha
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Correspondence to Houssem Jerbi.

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Jerbi, H., Braiek, N.B. & Bacha, A.B.B. A Method of Estimating the Domain of Attraction for Nonlinear Discrete-Time Systems. Arab J Sci Eng 39, 3841–3849 (2014). https://doi.org/10.1007/s13369-014-0947-4

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  • DOI: https://doi.org/10.1007/s13369-014-0947-4

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