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Guaranteed Cost and Finite-Time Non-fragile Control of Fractional-Order Positive Switched Systems with Asynchronous Switching and Impulsive Moments

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Abstract

This paper considers the problem of guaranteed cost and finite-time non-fragile control for a class of fractional-order positive switched systems with asynchronous switching and impulsive moments. Firstly, a novel cost function is presented. The sufficient conditions for the guaranteed cost and finite-time stability of the considered systems are derived via linear programming, using linear co-positive Lyapunov functions, the average dwell time method, and the average impulsive interval approach. Secondly, the finite-time and finite-time non-fragile controllers are designed to ensure that the corresponding closed-loop system is finite-time stable with a certain cost upper bound. Finally, an example of a fractional-order electrical circuit is provided, proving the proposed method’s feasibility and effectiveness.

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Acknowledgements

The authors are thankful for the financial support of this study by the National Natural Science Foundation of China (U1404610 and 61773350), the Scientific and Technological Innovation Leaders in Central Plains (Grant No. 194200510012), and the Science and Technology Innovative Teams at the University of Henan Province (Grant No. 18IRTSTHN011).

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Authors and Affiliations

  1. School of Information Engineering, Henan University of Science and Technology, Luoyang, 471023, China

    Leipo Liu, Yifan Di, Yilin Shang, Zhumu Fu & Bo Fan

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  1. Leipo Liu
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  2. Yifan Di
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  3. Yilin Shang
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  4. Zhumu Fu
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Correspondence to Leipo Liu.

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Liu, L., Di, Y., Shang, Y. et al. Guaranteed Cost and Finite-Time Non-fragile Control of Fractional-Order Positive Switched Systems with Asynchronous Switching and Impulsive Moments. Circuits Syst Signal Process 40, 3143–3160 (2021). https://doi.org/10.1007/s00034-020-01618-0

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  • DOI: https://doi.org/10.1007/s00034-020-01618-0

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