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Guaranteed cost control of fractional-order switched systems with mixed time-varying delays

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Abstract

This research paper investigates the problem of guaranteed cost control for a specific class of fractional-order switched systems characterized by both discrete and distributed time delays. By employing the linear matrix inequality (LMI) approach combined with the refined fractional-order Razumikhin theorem, a constructive geometric design of switching laws is developed to design a guaranteed cost controller ensuring the closed loop system not only asymptotically stable but also guarantees an adequate level of performance. The obtained conditions are dependent on the delays arising from the upper bound of the distributed time delays. These conditions are formulated in the form of linear matrix inequalities, which offers the advantage of efficient solvability using established convex algorithms. Two numerical examples with simulation results are provided to validate the efficacy of the proposed approach.

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Acknowledgements

The author would like to thank the editor(s) and anonymous reviewers for their constructive comments which helped to improve the present paper. This research was supported by Project of the TNU-University of Sciences in Vietnam under Grant number CS2022-TN06-02.

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Authors and Affiliations

  1. Department of Mathematics and Informatics, TNU–University of Sciences, Thai Nguyen, Vietnam

    Nguyen Thi Thanh Huyen & Mai Viet Thuan

  2. School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, 01 Dai Co Viet str., Hai Ba Trung District, Hanoi, Vietnam

    Nguyen Truong Thanh

  3. Department of Basic Sciences, Thai Nguyen University of Economics and Business Administration, Thai Nguyen, Vietnam

    Tran Nguyen Binh

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  1. Nguyen Thi Thanh Huyen
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  2. Mai Viet Thuan
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  3. Nguyen Truong Thanh
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  4. Tran Nguyen Binh
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Correspondence to Mai Viet Thuan.

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Communicated by Vasily E. Tarasov.

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Huyen, N.T.T., Thuan, M.V., Thanh, N.T. et al. Guaranteed cost control of fractional-order switched systems with mixed time-varying delays. Comp. Appl. Math. 42, 370 (2023). https://doi.org/10.1007/s40314-023-02505-5

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  • DOI: https://doi.org/10.1007/s40314-023-02505-5

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