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Mixed \(H_{\infty }\) and Passive Control for Fractional-Order Nonlinear Systems Via LMI Approach

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Abstract

This the first time that the problem of global asymptotic stability analysis, and mixed \(H_{\infty }\) and passive control for a class of control fractional-order nonlinear systems has been studied in this paper. By using the Lyapunov direct method and some properties of fractional calculate, we propose sufficient conditions to ensure the unforced system to be asymptotically stable with mixed \(H_{\infty }\) and passivity performance level. Further, mixed \(H_{\infty }\) and passive control design with an appropriate gain matrix has been derived to achieve the stabilization for fractional-order system with nonlinear perturbations and order \(0 < \alpha < 1\). These conditions are in the form of linear matrix inequalities, which therefore can be efficiently solved by using existing convex algorithms. The effectiveness of our results is illustrated through three numerical examples.

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Acknowledgements

The authors sincerely thank the Associate Editor and anonymous reviewers for their constructive comments that helped improve the quality and presentation of this paper. The research of Mai Viet Thuan is funded by the Ministry of Education and Training of Vietnam under grant leading by Dr. Mai Viet Thuan, Thai Nguyen University of Sciences, Decision number 106/Q-BGDT 13/01/2020.

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Authors and Affiliations

  1. Department for Management of Science and Technology Development, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Dinh Cong Huong

  2. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Dinh Cong Huong

  3. Department of Mathematics and Informatics, Thainguyen University of Sciences, Thainguyen, Vietnam

    Mai Viet Thuan

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  1. Dinh Cong Huong
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  2. Mai Viet Thuan
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Correspondence to Mai Viet Thuan.

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Huong, D.C., Thuan, M.V. Mixed \(H_{\infty }\) and Passive Control for Fractional-Order Nonlinear Systems Via LMI Approach. Acta Appl Math 170, 37–52 (2020). https://doi.org/10.1007/s10440-020-00323-z

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