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New Criteria for Guaranteed Cost Control of Nonlinear Fractional-Order Delay Systems: a Razumikhin Approach

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Abstract

The Krasovskii–Lyapunov second method provides a powerful approach to stability analysis of nonlinear systems; however, it is not always effectively applied for fractional-order systems (FOSs) with delay. In this paper, we investigate the problem of guaranteed cost control of fractional-order delay systems subject to nonlinear perturbations and parametric time-varying uncertainties. By using fractional Razumikhin theorem, new sufficient conditions are derived for designing a guaranteed cost controller, which not only makes the closed-loop system asymptotically stable but also guarantees an adequate cost level of performance. Compared with the existing results on the integer-order control systems, our results are more effective and convenient for testing and application. The proposed approach allows us to derive stability criteria of linear uncertain FOSs with delay. Finally, numerical examples are given to show the effectiveness of the obtained results.

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Acknowledgements

The authors would like to thank anonymous reviewers for their valuable comments, which allowed us to improve the paper.

Funding

This work was supported by the National Foundation for Science and Technology Development of Vietnam, grant 101.01-2017.300.

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Authors and Affiliations

  1. Institute of Mathematics, VAST, 18 Hoang Quoc Viet Road, Hanoi, 10307, Vietnam

    Vu Ngoc Phat

  2. Department of Mathematics and Informatics, Thainguyen University of Sciences, Thai Nguyen, Vietnam

    Mai Viet Thuan

  3. Faculty of Basic Science, Hung Yen University of Technology and Education, Hung Yen, Vietnam

    Tran Ngoc Tuan

Authors
  1. Vu Ngoc Phat
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  2. Mai Viet Thuan
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  3. Tran Ngoc Tuan
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Correspondence to Vu Ngoc Phat.

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Phat, V.N., Thuan, M.V. & Tuan, T.N. New Criteria for Guaranteed Cost Control of Nonlinear Fractional-Order Delay Systems: a Razumikhin Approach. Vietnam J. Math. 47, 403–415 (2019). https://doi.org/10.1007/s10013-018-0323-x

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  • DOI: https://doi.org/10.1007/s10013-018-0323-x

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