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A Novel Strategy of Extending the Domain of Attraction of Affine Nonlinear Systems

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Abstract

In this paper, a novel strategy of extending the domain of attraction of an asymptotically stable, affine nonlinear system is proposed. This method is based on the concept of mapping and relies on the asymptotic stability of a nonlinear system image via a continuous and injective mapping. The goal of designing the controller is to map the domain of attraction of an open-loop system into a larger domain, which is the domain of attraction of a closed-loop system. To find a suitable mapping that can make desired changes in the shape and size of domain of attraction, a criterion is obtained and its implementation instruction is demonstrated by examples. Results of simulation provided demonstrate the efficiency of the method proposed.

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Authors and Affiliations

  1. University of Tabriz, Tabriz, Iran

    M. Yadipour, F. Hashemzadeh & M. Baradarannia

Authors
  1. M. Yadipour
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  2. F. Hashemzadeh
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  3. M. Baradarannia
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Correspondence to M. Yadipour.

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 178, Optimal Control, 2020.

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Yadipour, M., Hashemzadeh, F. & Baradarannia, M. A Novel Strategy of Extending the Domain of Attraction of Affine Nonlinear Systems. J Math Sci 276, 289–299 (2023). https://doi.org/10.1007/s10958-023-06741-2

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