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On design of adaptive impulsive observer based on comparison system: modifications in stability theory and feasibility centralization

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Abstract

In this paper, an adaptive impulsive observer (AIO) for a class of uncertain nonlinear systems is proposed. There were several difficulties in the stability theory in Ayati and Khaloozadeh (IEEE Trans Circuits Syst I Regul Pap 59:179–187, 2012), which this study resolves. The stability theorem of the AIO is presented by employing the Lyapunov approach and the comparison system theory. Based on this novel theorem, the asymptotic stability of the recommended observer is ensured through well-defined sufficient conditions with less conservatism. The conditions are obtained in terms of Linear Matrix Inequalities (LMI), which have the great advantage computationally. By the mentioned AIO, the update equation of the unknown parameters contains the impulsive portions. Therefore, the convergence speed of the parameters estimation increases. According to the theorem, the maximum impulse time interval is determined efficiently. The speed control of the mapping from moments before impulse to impulse time is added to the AIO as a new feature that provides feasible LMIs with vaster region of the attractions. This AIO performed observation of a nonlinear and chaotic Lorenz system. The simulation results validate its efficiency.

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Authors and Affiliations

  1. Department of Systems and Control Engineering, K.N. Toosi University of Technology, Seyed-khandan, 1969764499, Tehran, Iran

    Nasrin Kalamain & Hamid Khaloozadeh

  2. School of Mechanical Engineering, College of Engineering, University of Tehran, Kargar, 1439955961, Tehran, Iran

    Moosa Ayati

Authors
  1. Nasrin Kalamain
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  2. Hamid Khaloozadeh
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  3. Moosa Ayati
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Nasrin Kalamian, Hamid Khaloozadeh, Moosa Ayati.

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Correspondence to Nasrin Kalamain.

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I declare that there is no conflict of interest in the publication of this article, and that there is no conflict of interest with any other author or institution for the publication of this article.

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I hereby declare that this manuscript is the result of our independent creation (me and my coauthors) under the reviewers’ comments. Except for the quoted contents, this manuscript does not contain any research achievements that have been published or written by other individuals or groups. I and Hamid Khaloozadeh and Moosa ayati are the authors of this manuscript. The legal responsibility of this statement shall be borne by me.

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Kalamain, N., Khaloozadeh, H. & Ayati, M. On design of adaptive impulsive observer based on comparison system: modifications in stability theory and feasibility centralization. Int. J. Dynam. Control 11, 149–161 (2023). https://doi.org/10.1007/s40435-021-00908-y

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  • DOI: https://doi.org/10.1007/s40435-021-00908-y

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