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Robust adaptive stabilization by high gain feedback for Markovian jump systems with partially unknown transition rates

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Abstract

In this paper, a class of multi-input multi-output nonlinearly perturbed Markovian jump systems with partially unknown transition rates is considered. We assume that this class of systems is characterized only by some structural properties such as the system is strongly minimum phase, with a strict relative degree one set and positive definite high frequency gain matrices. For this class of systems, a universal adaptive high gain controller, which is not based on estimation algorithms or identification of parameters, is designed such that in the presence of certain nonlinear perturbations and external disturbances, the convergence and the boundedness of the closed-loop system signals in the mean square sense are ensured. A vertical take-off and landing (VTOL) helicopter example is provided to demonstrate the performance and effectiveness of the obtained results.

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Code Availability Statement

The commercial software Matlab was used to carry out simulations and most of the calculations.

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Funding

No funding was received for conducting this study.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, University Chouaib Doukkali, B.P 20, 24000, El Jadida, Morocco

    Driss Berdouzi, Kamal El Hadri & Abdelmoula El Bouhtouri

Authors
  1. Driss Berdouzi
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  2. Kamal El Hadri
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  3. Abdelmoula El Bouhtouri
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Contributions

All authors contributed to the design and implementation of the research, to the analysis of the results and to the writing of the manuscript.

Corresponding author

Correspondence to Driss Berdouzi.

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Berdouzi, D., El Hadri, K. & El Bouhtouri, A. Robust adaptive stabilization by high gain feedback for Markovian jump systems with partially unknown transition rates. Int. J. Dynam. Control 10, 857–869 (2022). https://doi.org/10.1007/s40435-021-00861-w

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  • DOI: https://doi.org/10.1007/s40435-021-00861-w

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